8.7 Expanding products of three binomials — Learn

Prerequisites: expanding a single bracket and collecting like terms.

By the end of this section you can: expand and simplify a product of three binomials.

Covers: A4.

Learn the method

A binomial has two terms. For three brackets, expand two brackets first, then multiply every resulting term by the third bracket.

Keep like terms together as you work. This reduces errors and makes the final expression easier to check.

First $(x+1)(x+2)=x^2+3x+2$. Then multiply each of those three terms by $(x+3)$.

This gives $x^3+3x^2+2x+3x^2+9x+6$, which collects to $x^3+6x^2+11x+6$.

Worked example. Expand $(x+1)(x+2)(x+3)$.

$(x+1)(x+2)=x^2+3x+2$ — expand the first pair.

$(x^2+3x+2)(x+3)$

$=x^3+3x^2+3x^2+9x+2x+6$ — multiply each term by each term.

$=x^3+6x^2+11x+6$ — collect like terms.

Watch out. A common error is to multiply only some terms by the third bracket. Multiply every term by each term, then collect matching powers.

You should now be able to

• expand and simplify a product of three binomials.