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CBSE Questions for Class 8 Maths Algebraic Expressions And Identities Quiz 1 - MCQExams.com
CBSE
Class 8 Maths
Algebraic Expressions And Identities
Quiz 1
Multiply : $$(a^2 + b)$$ and $$ (a + b^2)$$
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$$a^2 + a^2b^2 + ab - b^3$$
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$$a^3 + a^2b^2 + ab + b^3$$
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$$a^3 + a^2b^2 - ab + b^3$$
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$$a^2 + a^2b^3 + ab + b^3$$
Explanation
$$(a^2 + b) (a + b^2)$$
$$=a^2(a+b^2)+b(a+b^2)$$
$$=a^3+a^2b^2+ab+b^3$$
Multiply $$(2x + 5)$$ and $$(4x-3)$$.
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$$4x^2 + 14x-15$$
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$$4x^2 + 14x+15$$
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$$8x^2 + 14x-15$$
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$$8x^2 + 14x+15$$
Explanation
$$(2x+5)\times (4x-3)$$
$$=2x(4x-3)+5(4x-3)$$
$$=8x^2-6x+20x-15$$
$$=8x^2+14x-15$$
Multiply: $$a + b, 7a^2b^2$$
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$$a^3b^6 + a^2b^3$$
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$$7a^3b^2 + 7a^2b^3$$
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$$7a^5b^2 + 3a^2b^3$$
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$$a^3b^2 + 7a3b^3$$
Explanation
$$a + b, 7a^2b^2$$
$$=(a + b)\times (7a^2b^2)$$
$$=7a^3b^2+7a^2b^3$$
Simplify:
$$5x(2x+3y)$$
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$$10x^2+15xy$$
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$$10x^4+15y$$
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$$10y^2+5xy$$
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$$10x^2+15x$$
Explanation
$$5x(2x+3y)$$
$$=10x^2+15xy$$
Evaluate using expansion of $$(a+b)^2$$ or $$(a-b)^2$$ :
$$(9.4)^2$$
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88.36
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88.46
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89.16
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89.56
Explanation
$${ (a+b) }^{ 2 }\quad =\quad a^{ 2 }+b^{ 2 }+2ab\\ a=9,\quad b=0.4\\ =\quad 9^{ 2 }+0.4^{ 2 }+2*9*0.4\\ =\quad 88.36$$
Obtain the product of:
$$2, 4y, 8y^2, 16y^3$$
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$$1024^6$$
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$$1000y^6$$
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$$1024y^5$$
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$$1024y^6$$
Explanation
$$2, 4y, 8y^2, 16y^3$$
$$=2\times 4y\times 8y^2\times 16y^3$$
$$=1024y^6$$
Simplify: $$(l + m)^2- 4lm$$
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$$(l -m)^2$$
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$$4l^2m^2$$
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$$(l+2m)^2$$
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$$(l-2m)^2$$
Explanation
$$(l+m)^2-4lm$$
$$=l^2+2lm+m^2-4lm$$
$$=l^2-2lm+m^2$$
$$=(l-m)^2$$
Multiply
$$(5-2x)$$ and $$ (3 + x)$$
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$$15-x+{2 x }^{ 2 }$$
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$$15-x-{ x }^{ 2 }$$
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$$15-x-{2 x }^{ 2 }$$
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$$15-x+{ x }^{ 2 }$$
Explanation
$$(5 -2x)\times (3 + x)$$
$$=5(3 + x)-2x(3 + x)$$
$$=15+5x-6x-2x^2$$
$$=15-x-2x^2$$
Find the value of $$2x\times 3x^3y^2\times3y^3z^2$$
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$$18x^4y^5z^2$$
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$$12x^4y^5z^2$$
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$$18x^2y^6z^2$$
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$$18x^4y^5z^3$$
Explanation
$$2x\times 3x^3y^2\times3y^3z^2$$
$$=(2\times 3\times 3)(x\times x^3)(y^2\times y^3)(z^2)$$
$$=18x^4y^5z^2$$, use $$a^m\times a^n=a^{m+n}$$
Find the product of the following pairs of monomials
$$4$$ & $$7p$$
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$$28p$$
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$$36p$$
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$$47p$$
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$$32p$$
Explanation
$$\begin{aligned}{}4 \times 7p &= \left( {4 \times 7} \right)p\\ &= 28p\end{aligned}$$
Obtain the product of: $$xy, yz, zx$$
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$$x^3y^2z^2$$
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$$x^2y^2y^2$$
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$$x^2y^2z^2$$
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$$x^2y^2y^y$$
Explanation
$$xy, yz, zx$$
$$=xy\times yz\times zx$$
$$=x^2y^2z^2$$
$$(2x + 3y)^{2} = 4x^{2} + 9y^{2} + M$$, find M.
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$$12xy$$
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$$10xy$$
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$$12$$
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$$10$$
Explanation
$$(2x + 3y)^{2} = 4x^{2} + 9y^{2} + 12xy$$, .................
$$(a+b)^2= a^2+2ab+b^2$$
hence, $$M = 12xy$$
Find the product of the following pairs of monomials.
$$4p, 7pq$$
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$$ p^2q$$
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$$ 28p^2q$$
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$$ 28pq$$
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$$ 28p^2$$
Explanation
$$4p, 7pq$$
The product of the monomial pair is,
$$=4\times p\times 7\times p\times q$$
$$=(4\times 7)\times(p\times p\times q)$$
$$=28p^2q$$
Find the product of the following pair of monomials.
$$4p$$ & $$7p$$
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$$ 28p+2$$
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$$ 28$$
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$$ 28p^2$$
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$$ 28p$$
Explanation
Given: $$4p, 7p$$
The product of the monomial pair is:
$$=4\times p\times 7\times p$$
$$=(4\times 7)\times(p\times p)$$
$$=28p^2$$
Find the product of the following pairs of monomials.
$$4p\ \&\ 0$$
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$$4p$$
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$$4$$
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4$$+$$p
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$$0$$
Explanation
$$4p, 0$$
The product of the monomial pair is,
$$=4\times p\times 0$$
$$=0$$
Find the product of the following pairs of monomials.
$$4p^3, 3p$$
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$$12p$$
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$$12p^4$$
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$$12p+4$$
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$$p^4$$
Explanation
$$4p^3, 3p$$
The product of the monomial pair is,
$$=4\times p\times p\times p\times 3\times p$$
$$=(4\times 3)\times(p\times p\times p\times p)$$
$$=12p^4$$
Obtain the product of:
$$m, mn, mnp$$
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$$ m^2n^3p$$
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$$ n^3m^2p$$
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$$ m^3n^2p$$
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$$ m^4n^2p$$
Explanation
$$m, mn, mnp$$
$$=m\times mn\times mnp$$
$$=m^3n^2p$$
The coefficient of $$x^2$$ in $$(2-3x^2) (x^2-5)$$ is :
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$$-17$$
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$$-10$$
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$$-3$$
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$$17$$
Explanation
$$(2-3x^2)(x^2-5)$$
$$=-3x^4+17x^2-10$$
A
Coefficient
is a constant number multiplied with a
variable.
Here as $$17$$ is multiplied with $$x^2$$. so it becomes the coefficient.
Hence, $$D$$ is the correct answer.
Multiply: $$
4p, q + r$$
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$$4r + 4pr$$
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$$4q + pr$$
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$$4p + pr$$
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$$4pq + 4pr$$
Explanation
$$4p, q + r$$
$$=4p\times( q + r)$$
$$=4pq+4pr$$
Multiply:
$$ 8ab^2 $$ by $$-4a^3b^4 $$ .
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$$-32a^4b^7 $$
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$$-32a^4b^6 $$
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$$-32a^4b^5 $$
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$$-32a^5b^6 $$
Explanation
$$8ab^2\times (-4a^3b^4)$$
$$=8\times (-4)a^{1+3}b^{2+4}$$
$$=-32a^4b^6$$
Multiply: $$ab, a b$$
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$$a^2b$$
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$$a^2b^2$$
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$$ab^3$$
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$$a^3b^3$$
Explanation
$$ab\times a b$$
$$={ a }^{ 1+1 }\times{ b }^{ 1+1 }$$
$$={ a }^{ 2 }{ b }^{ 2 }$$
Find the product of
$$x ,x^2, x^3 ,x^4$$
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$$x^{11}$$
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$$x^{8}$$
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$$x^{9}$$
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$$x^{10}$$
Explanation
The exponent or product rule states that while multiplying two powers having the same base, we have to add the exponents.
$$\Rightarrow x\times x^2\times x^3\times x^4$$
$$\Rightarrow x^{1+2+3+4}$$
$$\Rightarrow x^{10}$$
The product of $$4x^2 - 7x + 19$$ and $$(- 2x)$$ when $$x= 0$$ is:
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$$19$$
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$$-38$$
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$$17$$
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$$0$$
Explanation
Any real number when multiplied by 0 gives 0.
Here at $$x=0$$, $$-2x = 0$$ and hence the result of multiplication will also be zero.
Simplify: $$5{ x }^{ 2 }(x+5)+25$$
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$$\\ 5{ x }^{ 3 }+25{ x }+25$$
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$$5{ x }^{ 3 }+50x$$
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$$5{ x }^{ 3 }+25{ x }^{ 2 }+25$$
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$$5{ x }^{ 3 }+25x$$
Explanation
$$5{ x }^{ 2 }(x+5)+25\\ =5{ x }^{ 3 }+25{ x }^{ 2 }+25$$
Multiply: $$a^2 -9, 4a$$
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$$4a^3 - 36a$$
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$$3a^3 - 36a$$
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$$3a^3 +36a$$
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$$4a^3 + 36a$$
Explanation
$$a^2- 9, 4a$$
$$=a^2- 9\times 4a$$
$$=4a^3-36a$$
State whether True or False.
Multiply: $$ -\dfrac{3}{2}x^5y^3 $$ and $$\dfrac{4}{9}a^2x^3y$$.
The answer is $$ -\dfrac{2}{3}a^2x^8y^4$$.
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True
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False
Explanation
$$-\frac{3}{2}x^5y^3 \times \frac{4}{9}a^2x^3y$$
$$=(-\frac{3}{2})(\frac{4}{9})ax^{5+3}y^(3+1)$$
$$=-\frac{2}{3}a^2x^8y^4$$
State whether True or False.
Multiply: $$ abx, -3a^2x $$ and $$ 7b^2x^3 $$.
The value is $$-21a^3b^3x^5 $$.
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True
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False
Explanation
$$(abx)\times (3a^2x)\times (7b^2x^3)$$
$$=(-3)(7)a^{1+2}b^{1+2}x^{1+1+3}$$
$$=-21a^3b^3x^5$$
State whether True or False.
On multiplying $$ a^2, ab$$ and $$ b^2 $$, we get
the answer as $$a^3b^3 $$.
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True
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False
Explanation
The given terms are $$a^2,\ ab$$ and $$b^2$$
On multiplying the given terms, we get:
$$a^2 \times ab \times b^2$$
Using the laws of exponent, we know that, $$a^m\times a^n=a^{m+n}$$
$$\therefore \ a^2 \times ab \times b^2=a^{2+1}b^{1+2}$$
$$\Rightarrow a^3b^3$$
$$\therefore \ a^2 \times ab \times b^2=a^3b^3$$
Hence, the given statement is true.
State whether True or False.
Multiply: $$ -3bx, -5xy $$ and $$ -7b^2x^3$$.
The answer is $$-105b^3x^5y $$.
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True
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False
Explanation
$$(3bx)\times (5xy)\times (7b^2x^3)$$
$$=(-3)(-5)(-7)b^{1+2}x^{1+1+3}y^{1}$$
$$=-105b^3x^5y$$
State whether True or False.
Multiply: $$ 2a^3-3a^2b $$ and $$-\dfrac{1}{2}ab^2 $$.
The value is $$-a^4b^2+\dfrac{3}{2}a^3b^3 $$.
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True
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False
Explanation
As given $$ 2a^3-3a^2b $$ and $$-\frac{1}{2}ab^2 $$
$$\Rightarrow 2a^{3}\times-\frac{1}{2}ab^{2} - 3a^{2}b\times-\frac{1}{2}ab^{2}$$
$$\Rightarrow -a^{3}\times ab^{2} + \frac{3}{2}a^{2}b\times ab^{2}$$
$$\Rightarrow -a^{3+1}b^{2}+\frac{3}{2}a^{2+1}b^{1+2}$$
$$\Rightarrow -a^{4}b^{2}+\frac{3}{2}a^{3}b^{3}$$
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