Question

factorise
x power 4 -81
​

Answer 1

Answer:

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

Step-by-step explanation:

Given \: x^{4}+4\\=\big(x^{2}\big)^{2}+9^{2}

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

Here, \\a = x^{2},\:b = 29

=\left(x^{2}+9\right)^{2}-2\times x^{2}\times 29

=\left(x^{2}+9\right)^{2}-4\times x^{2}

=\left(x^{2}+9\right)^{2}-(9x)^{2}

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

=(x^{2}+9+9x)(x^{2}+9-9x)

=(x^{2}+9x+9)(x^{2}-9x+9)

Therefore,.

x^{4}+81=(x^{2}+9x+9)(x^{2}-9x+9)

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Step-by-step explanation: