Question

$\text{Factorise}:m^4-256$.

• A. $(m-8)(m+8)(m^2+16)$
• B. $(m-4)(m+4)(m^2+4)$
• C. $(m-4)(m+4)(m^2+16)$
• D. $(m-4)(m+4)(m^2+8)$

Answer 1

The correct option is C $(m-4)(m+4)(m^2+16)$

$\text{Using the identity:}{a}^2-b^2=(a+b)(a-b),$
$m^4-256=(m^2{)}^2-(16{)}^2$
Hence, the above expression can be written as,
$(m^2{)}^2-(16{)}^2=(m^2+16)(m^2-16)$
$=(m^2+16)(m^2-4^2)$
$[\text{Using the identity:}{a}^2-b^2=(a+b\left)\right(a-b\left)\right],$
$=(m^2+16)(m+4)(m-4)$
$=(m-4)(m+4)(m^2+16)$