Question

4x^4+1 factorise the following algebraic expression

Answer 1

Answer

4x^2+4x+1

4x^2+2x+2x+1

2x(2x+1)+1(2x+1)

( 2x+1)(2x+1)

Therefore x = -1/2 and -1/2( equal roots )

Answer 2

As we know that,
$\: \: \: \: \: \: \: ({a} + {b})^{2} = {a}^{2} + {b}^{2} + 2ab \\ = >{a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab$
So,
$= > {4x}^{4} + 1 \\ = {( {2x}^{2}) }^{2} + {1}^{2} \\ = {( 2{x}^{2} + 1)}^{2} - 8 {x}^{2} \\ = {( {2x}^{2} + 1)}^{2} - { (\sqrt{8}x)}^{2}$
As we know that,
$(a + b)(a - b) = {a}^{2} - {b}^{2}$
So,
$= > {(2 {x}^{2} + 1) }^{2} - {( \sqrt{8}x) }^{2} \\ = (2 {x}^{2} + 1 + \sqrt{8}x)(2 {x}^{2} + 1 - \sqrt{8}x)$



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