Question

Which expression is a difference of squares?

Answer 1

Answer: 100 $x^{2}$ - 49 $y^{2}$

Step-by-step explanation:

Answer 2

Answer:

$100 x^{2}-49 y^{2}$ can be written in the difference of squares.

Option: D

Step-by-step explanation:

We know that $a^{2}-b^{2}=(a-b)(a+b)$

Take the equation $100 x^{2}-49 y^{2}$ and can be written as follows.

$\left(100 x^{2}-49 y^{2}\right)=\left\{(10 x)^{2}-(7 y)^{2}\right\}$

100 is the square of 10

49 is the square of 7

$x^{2}$ is the square of x

$y^{2}$ is the square of y

Thus we can write the $100 x^{2}-49 y^{2}$ as the difference of squares.

$\left(100 x^{2}-49 y^{2}\right)=\left\{(10 x)^{2}-(7 y)^{2}\right\}$

By using the formula $a^{2}-b^{2}=(a-b)(a+b)$ we can write  $\left\{(10 x)^{2}-(7 y)^{2}\right\}$ as

$\left\{(10 x)^{2}-(7 y)^{2}\right\}$ $=(10 x-7 y)(10 x+7 y)$