Question

Which option is equal to the square of $9x-7xy$.

• A. $81x^2+49x^2{y}^2$
• B. $81x^2-49x^2{y}^2$
• C. $81x^2+49x^2{y}^2-63x^{2}y$
• D. $81x^2+49x^2{y}^2-126x^{2}y$

Answer 1

The correct option is D

$81x^2+49x^2{y}^2-126x^{2}y$

Finding the square of a number:

Given:, $9x-7xy$

Now, square of $9x-7xy$ is ${(9x-7xy)}^2$

Using identity: ${\left(a-b\right)}^2=a^2-2ab+b^2$

where $a=9x$and $b=7xy$, we get

$$\begin{gathered} {\left(9x-7xy\right)}^2={\left(9x\right)}^2-2\times 9x\times 7xy+{\left(7xy\right)}^2 \\ \Rightarrow {\left(9x-7xy\right)}^2=81x^2-126x^{2}y+49x^{2}y \end{gathered}$$

Hence, D is the correct option.