Question

The expression $x^4+8x^2+16$ can be factorised as

• A. $(x^2+x+16{)}^2$
• B. $(x^2+x+1{)}^2$
• C. $(x^2+4{)}^2$
• D. $(x^2+x-4)(x^2-x+4)$

Answer 1

The correct option is C

$(x^2+4{)}^2$

$x^4+8x^2+16$

= $(x^2{)}^2+8x^2+4^2$

= $(x^2{)}^2+(2\times x^2\times 4)+4^2$

Using $(a+b{)}^2=a^2+2ab+b^2$, the above expression can be written as

$(x^2+4{)}^2$

Therefore, $x^4+8x^2+16$ = $(x^2+4{)}^2$