How do you multiply (2-x)^3(2−x)3?

1 Answer
Leland Adriano Alejandro
Jul 17, 2016

(2-x)^3=8-12x+6x^2-x^3(2−x)3=8−12x+6x2−x3

Explanation:

To multiply (2-x)^3(2−x)3, we have several ways to do it. One solution is by Binomial Theorem and another is by simply multiplying the expression (2-x)(2−x) by itself and the result by itself again.

Solution by Binomial Theorem

(a-b)^3=a^3-3a^2b+3ab^2-b^3(a−b)3=a3−3a2b+3ab2−b3

So that

(2-x)^3=2^3-3(2)^2*x+3(2)(x^2)-x^3(2−x)3=23−3(2)2⋅x+3(2)(x2)−x3

(2-x)^3=8-12x+6x^2-x^3(2−x)3=8−12x+6x2−x3

Solution by multiplication

(2-x)^3=(2-x)(2-x)(2-x)(2−x)3=(2−x)(2−x)(2−x)

(2-x)^3=[2(2-x)-x(2-x)]*(2-x)(2−x)3=[2(2−x)−x(2−x)]⋅(2−x)

(2-x)^3=[4-2x-2x+x^2]*(2-x)(2−x)3=[4−2x−2x+x2]⋅(2−x)

(2-x)^3=[4-4x+x^2]*(2-x)(2−x)3=[4−4x+x2]⋅(2−x)

(2-x)^3=[4*(2-x)-4x*(2-x)+x^2*(2-x)](2−x)3=[4⋅(2−x)−4x⋅(2−x)+x2⋅(2−x)]

(2-x)^3=[8-4x-8x+4x^2+2x^2-x^3](2−x)3=[8−4x−8x+4x2+2x2−x3]

(2-x)^3=8-12x+6x^2-x^3(2−x)3=8−12x+6x2−x3

God bless....I hope the explanation is useful.

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