How do you multiply #(2-x)^3#?

1 Answer

Answer:

#(2-x)^3=8-12x+6x^2-x^3#

Explanation:

To multiply #(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)# by itself and the result by itself again.

Solution by Binomial Theorem

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

So that

#(2-x)^3=2^3-3(2)^2*x+3(2)(x^2)-x^3#

#(2-x)^3=8-12x+6x^2-x^3#

Solution by multiplication

#(2-x)^3=(2-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=[4-4x+x^2]*(2-x)#

#(2-x)^3=[4*(2-x)-4x*(2-x)+x^2*(2-x)]#

#(2-x)^3=[8-4x-8x+4x^2+2x^2-x^3]#

#(2-x)^3=8-12x+6x^2-x^3#

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