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Factorise :x power4+4

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Factorise :x power4+4

Posted by Prince Raj 5 years, 1 month ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 5 years, 1 month ago

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

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

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

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

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

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

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

$=(x^{2}+2+2x)(x^{2}+2-2x)$

$=(x^{2}+2x+2)(x^{2}-2x+2)$

Therefore,.

$x^{4}+4=(x^{2}+2x+2)(x^{2}-2x+2)$

1Thank You

ANSWER

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