Question

Factorize the expression: $1-25(a+b{)}^2$

• A. (1-5a-5b)(1+5a-5b)
• B. (1-5a-5b)(1+5a+5b)
• C. (1+5a+5b)(1+5a+5b)
• D. (1-5a-5b)(1-5a-5b)

Answer 1

The correct option is B $(1-5a-5b)(1+5a+5b)$

The given expression is$1-25(a+b{)}^2$, which can be written as,

$=1^2-\left[5\right(a+b){]}^2$

Using the identity $x^2-y^2=(x+y)(x-y)$

$=(1-[5(a+b)\left]\right)(1+[5(a+b)\left]\right)$

$=(1-5a-5b)(1+5a+5b)$