Question

Factorise: $1-16(x-2y{)}^2$.

• A. $[1-4x-8y][1+4x-8y]$
• B. $[1-4x-8y][1+4x+8y]$
• C. $[1+4x+8y][1+4x+8y]$
• D. $[1-4x+8y][1+4x-8y]$

Answer 1

The correct option is D

$[1-4x+8y][1+4x-8y]$

Given: $1-16(x-2y{)}^2$
The expression can be written as $1^2-\left[4\right(x-2y){]}^2$.
Using the identity:$a^2-b^2=(a+b)(a-b)$

$=[1-\overline{4(x-2y)}][1+\overline{4(x-2y)}]$

$=[1-4x+8y][1+4x-8y]$