Question

Which of the following is/are the factors of the algebraic expression: $(2x+7y{)}^2-(7x-2y{)}^2$?

• A. 9x + 5y
• B. 9y - 5x
• C. 5x - 7y
• D. 7x - 5y

Answer 1

Answer: (A), (B)

The correct options are
A 9x + 5y
B 9y - 5x

We can factorise the expression, $(2x+7y{)}^2-(7x-2y{)}^2$, by using the identity $(a^2-b^2)=(a+b)(a-b).$

Let $(2x+7y)$ be $a$ and $(7x-2y)$ be b.

$(2x+7y{)}^2-(7x-2y{)}^2=\left(\right(2x+7y)+(7x-2y\left)\right)\left(\right(2x+7y)-(7x-2y\left)\right)=(9x+5y)(9y-5x)$

Hence, the facotors of the expression are (9x + 5y) and (9y - 5x).