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Factor the expression by treating it as the difference of two squares, (x3)2-1

User Ken Liu
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1 Answer

5 votes

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


User Armando Ramirez
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8.3k points

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