Question

Which of the following represents the factorisation of the expression
$a^4+2a^2{b}^2+b^4?$

• A. $(a^2+b^2)$
• B. $(a^2+b^2{)}^2$
• C. $(a^2-b^2{)}^2$
• D. $(a^2-b^2)$

Answer 1

The correct option is B $(a^2+b^2{)}^2$

$\text{Given, the expression is}{a}^4+2a^2{b}^2+b^4.$

$\text{The above expression can be}\text{written as,}{a}^4+2a^2{b}^2+b^4=(a^2{)}^2+2a^2{b}^2+(b^2{)}^2$

$\text{Using the identity:}(a+b{)}^2=a^2+2ab+b^2,\text{we get,}(a^2{)}^2+2a^2{b}^2+(b^2{)}^2=(a^2+b^2{)}^2$