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Factorise :x power4+4

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Factorise :x power4+4

Posted by Prince Raj 5 years, 8 months ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 5 years, 8 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

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Posted by Sheikh Alfaz 1 month, 2 weeks ago

CBSE > Class 09 > Mathematics

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Don't post personal information, mobile numbers and other details.
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Be nice and polite and avoid rude and abusive language. Avoid inappropriate language and attention, vulgar terms and anything sexually suggestive. Avoid harassment and bullying.
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Posted by Yash Pandey 6 months ago

CBSE > Class 09 > Mathematics