How do you multiply (x-3)^3(x3)3?

2 Answers
Apr 24, 2017

See the entire solution process below:

Explanation:

We can rewrite this expression as:

(x - 3)(x - 3)(x - 3)(x3)(x3)(x3)

We can multiple the two terms in parenthesis on the right of the expression using this rule:

(a - b)(a - b) = a^2 - 2ab + b^2(ab)(ab)=a22ab+b2

Substituting xx for aa and 33 for bb gives:

(x - 3)(x - 3)(x - 3) = (x - 3)(x^2 - (2x * 3) + 9) =(x3)(x3)(x3)=(x3)(x2(2x3)+9)=

(x - 3)(x^2 - 6x + 9)(x3)(x26x+9)

We now need to multiply these two terms together. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

(color(red)(x) - color(red)(3))(color(blue)(x^2) - color(blue)(6x) + color(blue)(9))(x3)(x26x+9) becomes:

(color(red)(x) xx color(blue)(x^2)) - (color(red)(x) xx color(blue)(6x)) + (color(red)(x) xx color(blue)(9)) - (color(red)(3) xx color(blue)(x^2)) + (color(red)(3) xx color(blue)(6x)) - (color(red)(3) xx color(blue)(9))(x×x2)(x×6x)+(x×9)(3×x2)+(3×6x)(3×9)

x^3 - 6x^2 + 9x - 3x^2 + 18x - 27x36x2+9x3x2+18x27

We can now group and combine like terms:

x^3 - 6x^2 - 3x^2 + 9x + 18x - 27x36x23x2+9x+18x27

x^3 + (-6 - 3)x^2 + (9 + 18)x - 27x3+(63)x2+(9+18)x27

x^3 + (-9)x^2 + 27x - 27x3+(9)x2+27x27

x^3 - 9x^2 + 27x - 27x39x2+27x27

Apr 24, 2017

x^3-9x^2+27x-27x39x2+27x27

Explanation:

(x-3)^3(x3)3 = (x-3)(x-3)(x-3)(x3)(x3)(x3)

Taking into account only the first two terms, we multiply to get x^2-6x+9x26x+9.

Next, we multiply x^2-6x+9x26x+9 by x-3x3.

The result is x^3-3x^2-6x^2+18x+9x-27x33x26x2+18x+9x27.

We simplify this by combining like terms:
x^3-9x^2+27x-27x39x2+27x27

And that is the answer.