How do you multiply (x−3)3?

Question

laiedkn · Accepted Answer

We can rewrite this expression as:
(x-3)(x-3)(x-3)
We can multiple the two terms in parenthesis on the right of the expression using this rule:

(a - b) (a - b) = a^{2} - 2 a b + b^{2}

Substituting x for a and 3 for b gives:

(x - 3) (x - 3) (x - 3) = (x - 3) (x^{2} - (2 x \cdot 3) + 9) =

(x - 3) (x^{2} - 6 x + 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.

(x - 3) (x^{2} - 6 x + 9)

becomes:

(x \times x^{2}) - (x \times 6 x) + (x \times 9) - (3 \times x^{2}) + (3 \times 6 x) - (3 \times 9)

x^{3} - 6 x^{2} + 9 x - 3 x^{2} + 18 x - 27

We can now group and combine like terms:

x^{3} - 6 x^{2} - 3 x^{2} + 9 x + 18 x - 27

x^{3} + (- 6 - 3) x^{2} + (9 + 18) x - 27

x^{3} + (- 9) x^{2} + 27 x - 27

x^{3} - 9 x^{2} + 27 x - 27

Amubbemibren3k · Accepted Answer

(x−3)3=(x−3)(x−3)(x−3)  Taking into account only the first two terms, we multiply to get x2−6x+9.  Next, we multiply x2−6x+9 by x-3.  The result is x3−3x2−6x2+18x+9x−27.  We simplify this by combining like terms:  x3−9x2+27x−27  And that is the answer.

How do you multiply (x-3)^{3}?

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