Math · College algebra · Worked example

Expand (x−2)³

Use coefficients, powers and signs together.

Read row three

The coefficients are 1,3,3,1.

{(a + b)}^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

Use b=−2, with parentheses.

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

The square contributes a positive term and the cube a negative term.

x^{3} - 6 x^{2} + 12 x - 8

(x−2)³=x³−6x²+12x−8.

Expand (x+3)² and identify the middle coefficient.

Show the answer and explanation

The binomial coefficient 2 multiplies x·3.

Change an input and predict the result before checking it.

Sources and scope

Authored study material. Tool results depend on the stated inputs and model assumptions.