Question

Which option is equal to the square of $3x-4y$.

• A. $9x^2–16y^2$
• B. $6x^2–8y^2$
• C. $9x^2+16y^2+24xy$
• D. $9x^2+16y^2–24xy$

Answer 1

The correct option is D

$9x^2+16y^2–24xy$

Given:

$3x-4y$

Square of $3x-4y$ is ${\left(3x-4y\right)}^2$

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

where $a=3x$and $b=4y$

$$\begin{gathered} \Rightarrow {\left(3x-4y\right)}^2={\left(3x\right)}^2-2\times 3x\times 4y+{\left(4y\right)}^2 \\ \Rightarrow {\left(3x-4y\right)}^2=9x^2-24xy+16y^2 \end{gathered}$$

Hence, D is the correct option.