Question

(21X^4 - 14x^2 + 7X) -7X^3

step by step explain please ​

Answer 1

Answer:

The factorisation of x^{4} -14x^{2} +1x

4

−14x

2

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

2

+1+4x)(x

2

+1−4x) .

Step-by-step explanation:

We have,

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

4

−14x

2

+1

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

4

−14x

2

+1=?

∴ (x^{4} +1)-14x^{2}(x

4

+1)−14x

2

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

2

)

2

+1

2

)−14x

2

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

2

+1)

2

−2x

2

−14x

2

[ ∵ a^{2} +b^{2} =(a+b)^{2} -2aba

2

+b

2

=(a+b)

2

−2ab

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

2

+1)

2

−16x

2

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

2

+1)

2

−(4x)x

2

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

2

+1+4x)(x

2

+1−4x)

[ ∵ a^{2} -b^{2}=(a+b)(a-b)a

2

−b

2

=(a+b)(a−b)

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

4

−14x

2

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

2

+1+4x)(x

2

+1−4x) .