Question

p^4+2p^2q^2+q^4 factorise​

Answer 1

Following are the steps for getting the answer:

Given:

$p^4+2p^2q^2+q^4$

to find:

Factor of $p^4+2p^2q^2+q^4$

Solution:

we have to find the factor of $p^4+2p^2q^2+q^4$

we can write this like

(p²)²+2p²q²+(q²)²

we know that,

(a+b)²=a²+2ab+b²

so,

=(p²+q²)²

=(p²+q²)(p²+q²)

thus, the Factor of $p^4+2p^2q^2+q^4$ is (p²+q²)(p²+q²)

Answer 2

Given expression: $p^{4} +2p^{2} q^{2} +q^{4}$.

We have to factorize the above expression.

$p^{4} +2p^{2} q^{2} +q^{4}$

$=(p^{2} \times p^{2} ) +(2\times p^{2} \times q^{2} )+ (q^{2} \times q^{2} )$

$=(p^{2} )^{2} +(2\times p^{2} \times q^{2} )+(q^{2} )^{2}$

Above expression is in the form of $a^{2} +2ab+b^{2}$.

We know that, $a^{2} +2ab+b^{2} =(a+b)^{2}$.

Here, $a=p^{2}$ and $b=q^{2}$.

$=(p^{2} +q^{2} )^{2}$

$=(p^{2} +q^{2} ) \times (p^{2} +q^{2} )$

$=(p^{2} +q^{2} ) (p^{2} +q^{2} )$.

Hence, $p^{4} +2p^{2} q^{2} +q^{4}$ $=(p^{2} +q^{2} ) (p^{2} +q^{2} )$.