Question

Factorise:

$16(a-b{)}^2-4(c-d{)}^2$

• A. $(4a+4b+2c-2d)(4a-b-2c+2d)$
• B. $(4a-b+2c-2d)(4a-4b-2c+2d)$
• C. $(4a-4b+2c-2d)(4a-4b-2c+2d)$
• D. $(a-4b+2c-2d)(a-4b-2c+2d)$

Answer 1

The correct option is C $(4a-4b+2c-2d)(4a-4b-2c+2d)$

$\begin{array}{cc}16{\left(a-b\right)}^2-4{\left(c-d\right)}^2& ={\left[4\left(a-b\right)\right]}^2-{\left[2\left(c-d\right)\right]}^2\\ & ={\left(4a-4b\right)}^2-{\left(2c-2d\right)}^2\\ & =\left(4a-4b+2c-2d\right)\left(4a-4b-2c+2d\right)\end{array}$

Hence, option $C$ is correct.