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Factorise :x power4+4

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Factorise :x power4+4

Posted by Prince Raj 4 years, 7 months ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 4 years, 7 months ago

{tex}Given \: x^{4}+4\\=\big(x^{2}\big)^{2}+2^{2}{/tex}

{tex}We \: know \: that ,\\\boxed {a^{2}+b^{2}=(a+b)^{2}-2ab}{/tex}

Here, {tex}\\a = x^{2},\:b = 2{/tex}

{tex}=\left(x^{2}+2\right)^{2}-2\times x^{2}\times 2{/tex}

{tex}=\left(x^{2}+2\right)^{2}-4\times x^{2} {/tex}

{tex}=\left(x^{2}+2\right)^{2}-(2x)^{2}{/tex}

{tex}We \: know \: that ,\\\boxed { a^{2}-b^{2}=(a+b)(a-b)}{/tex}

{tex}=(x^{2}+2+2x)(x^{2}+2-2x){/tex}

{tex}=(x^{2}+2x+2)(x^{2}-2x+2){/tex}

Therefore,.

{tex}x^{4}+4=(x^{2}+2x+2)(x^{2}-2x+2){/tex}

1Thank You

ANSWER

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Posted by T Prudhvi 1 week, 2 days ago

CBSE > Class 09 > Mathematics