Explanation
3912=(400−9)2It is the form of (a−b)2, where a=400,b=9Applying the formula (a−b)2=a2+b2−2ab3912=(400−9)2=4002+92−2×400×9=1,60,000+81−7200=152881
607 can be written as 600+7
∴It is the form of {(a+b)}^{2} , where a = 600, b = 7 Applying the formula { (a+b) }^{ 2 } = {a}^{2} + { b }^{ 2 } + 2ab {607}^{2} = {(600 + 7)}^{2} = {600}^{2} + { 7 }^{ 2 } +2\times 600 \times 7 = 360000 + 49 + 8400 = 368449
Given, (4a+3b)^{2} -(4a-3b)^{2}+48 ab.
We know, (a+b)^2=a^2+2ab+b^2
and (a-b)^2=a^2-2ab+b^2.
Given, \left(\dfrac{2x}{7}-\dfrac{7y}{4}\right)^{2}.
We know, (a-b)^2=a^2+2ab+b^2.
Then,
\left(\dfrac{2x}{7}-\dfrac{7y}{4}\right)^{2}
=(\dfrac{2x}{7})^2-2(\dfrac{2x}{7})(\dfrac{7y}{4})+(\dfrac{7y}{4})^2
=\dfrac{4x^{2}}{49}- xy+ \dfrac{49y^{2}}{16} .
Therefore, ption C is correct.
Given, \left(\dfrac{7}{8}{x}+\dfrac{4}{5}{y}\right )^{2}.
We know, (x+y)^2=x^2+2xy+y^2.
\left(\dfrac{7}{8}{x}+\dfrac{4}{5}{y}\right )^{2}
=(\dfrac{7}{8}{x})^2+2(\dfrac{7}{8}{x})(\dfrac{4}{5}{y})+(\dfrac{4}{5}{y})^2
=\dfrac{49}{64}{x^{2}} +\dfrac{7}{5}{xy}+\dfrac{16}{25}{y^{2}} .
Therefore, option D is correct.
Find the missing term in the following problem:
\left(\displaystyle \frac{3x}{4}\, -\, \displaystyle \frac{4y}{3} \right )^2\, =\, \displaystyle \frac{9x^2}{16}\, +\, ..........\, +\, \displaystyle \frac{16y^2}{9}.
Given, \left(\displaystyle \frac{3x}{4}\, -\, \displaystyle \frac{4y}{3} \right )^2\, .
We know, (a-b)^2=a^2-2ab+b^2.
\left(\displaystyle \frac{3x}{4}\, -\, \displaystyle \frac{4y}{3} \right )^2\,
=\left( \displaystyle \frac{3x}{4} \right )^2\, -\, 2\, \left(\displaystyle \frac{3x}{4} \right )\left(\displaystyle \frac{4y}{3} \right )\, +\, \left(\displaystyle \frac{4y}{3}\right)^2
=\, \displaystyle \frac{9x^2}{16}\, -\, 2xy\, +\, \displaystyle \frac{16y^2}{9}
=\, \displaystyle \frac{9x^2}{16}\, +\, (-\, 2xy)\, +\, \displaystyle \frac{16y^2}{9}.
Hence, the missing term is -2xy.
Therefore, option B is correct.
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