Question

Factorise : x^4 + 16x^2 - 80​

Answer 1

Answer: Hi mate.....

The factorisation of x^{4} -14x^{2} +1 is (x^{2}+1+4x)(x^{2}+1-4x).

Step-by-step explanation:

We have,

x^{4} -14x^{2} +1

To find, the factorisation of x^{4} -14x^{2} +1=?

∴ (x^{4} +1)-14x^{2}

=((x^{2})^{2} +1^{2} )-14x^{2}

=(x^{2}+1)^{2} -2x^{2}-14x^{2}

[ ∵ a^{2} +b^{2} =(a+b)^{2} -2ab]

=(x^{2}+1)^{2} -16x^{2}

=(x^{2}+1)^{2} -(4x)x^{2}

=(x^{2}+1+4x)(x^{2}+1-4x)

[ ∵ a^{2} -b^{2}=(a+b)(a-b)]

Hence, the factorisation of x^{4} -14x^{2} +1 is (x^{2}+1+4x)(x^{2}+1-4x)