Factor the expression by treating it as the difference

Ответ:

kbuhvu

11.03.2022

we are given

(x^3)^2-1

Let's assume x^3 as a

(x^3)^2-1=a^2-1

now, we can factor

and we get

a^2-1=(a-1)(a+1)

now, we can plug back 'a'

and we get

(x^3)^2-1=(x^3-1)(x^3+1)

now, we can factor again

we know that

a^3+b^3=(a+b)(a^2-ab+b^2)

so, we get

(x^3)^2-1=(x^3-1)(x+1)(x^2-x+1)

now, we can use formula

a^3-b^3=(a-b)(a^2+ab+b^2)

we can plug it

(x^3)^2-1=(x-1)(x^2+x+1)(x+1)(x^2-x+1)

we can rearrange it

(x^3)^2-1=(x-1)(x+1)(x^2-x+1)(x^2+x+1) ..............Answer

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