Question

Factorize
${a}^{4} + 2 {a}^{2} {b}^{2} + {b}^{2}$
​

Answer 1

Correct Question

${a}^{4} + 2 {a}^{2} {b}^{2} + {b}^{4}$

Solution

we know that

$\color{brown} {a}^{2} + 2 {a}^{} {b}^{} + {b}^{2}$=$\color{red}{(a+b)}^2$(also real it from this)

Now we factorise the actual question

$\implies {a}^{4} + 2 {a}^{2} {b}^{2} + {b}^{4}$

$\implies {a}^{4} + {a}^{2} {b}^{2}+ {a}^{2} {b}^{2} + {b}^{4}$

$\implies {a}^{4} + {a}^{2} {b}^{2}+ {a}^{2} {b}^{2} + {b}^{4}$

Now taking common a² and b²

Then,

$\implies$a²(a²+b²)+b²(a²+b²)

$\implies$(a²+b²)(a²+b²)

Hence,the factorisation will be (a²+b²)(a²+b²)

Answer 2

$</p><p>\tt{\huge {\pink {Hello!!! }}}$

$</p><p></p><p>\tt{\red{Correction \: - }}$

$\tt{ \purple{ \implies{ {a}^{4} + 2 {a}^{2} {b}^{2} \: + \: {b}^{4} }}}$

$\tt{ \orange{ \implies {({ {a}^{2}) }^{2} + 2 { a }^{2} {b}^{2} \: + {( {b}^{2} )}^{2} = {( {a}^{2} + {b}^{2} )}^{2} }}}$

Hence Factorised.