Question

The factors of $x^4+y^4+x^2{y}^2$ is

• A. $(x^2+y^2)(x^2+y^2–xy)$
• B. $(x^2+y^2)(x^2–y^2)$
• C. $(x^2+y^2+xy)(x^2+y^2–xy)$
• D. Factorisation is not possible

Answer 1

The correct option is C

$(x^2+y^2+xy)(x^2+y^2–xy)$

The given algebraic expression is $x^4+y^4+x^2{y}^2$

$$\begin{gathered} \therefore x^4+y^4+x^2{y}^2=(x^4+y^4+2x^2{y}^2)–x^2{y}^2 \\ ={(x^2+y^2)}^2–x^2{y}^2[byu\sin gformula{a}^2+b^2+2ab={\left(a+b\right)}^2] \\ ={(x^2+y^2)}^2–{\left(xy\right)}^2 \end{gathered}$$

$=(x^2+y^2+xy)(x^2+y^2–xy)$ Use formula $a^2–b^2=(a-b)(a+b)$

Hence, the factors of $x^4+y^4+x^2{y}^2$ is $(x^2+y^2+xy)(x^2+y^2–xy)$

Hence, the correct option is (C).