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Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus

Multiplying a binomial by a trinomial

  • Grade 10
  • Foundations of Mathematics and Pre Calculus
  • 2 min 18 s
  • British Columbia
  • BC10-MA-29

Using (x + 2)(x² − 3x + 4), the video explains terms, binomials and trinomials, then uses a grid to multiply each of the 2 terms by each of the 3 terms, which gives six products and shows how missing one leaves an empty box. It collects the like terms to reach x³ − x² − 2x + 8, checks that both sides equal 8 when x = 2, and ends on the recap "Multiply every term, then collect like terms."

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In one sentence

The question this lesson answers

How do we multiply x plus 2 by x squared minus 3x plus 4?

Each part, together with its sign, is called a term.

Transcript

What the lesson says

How do we multiply x plus 2 by x squared minus 3x plus 4?

Each part, together with its sign, is called a term.

x plus 2 has two terms, so it is a binomial. x squared minus 3x plus 4 has three terms, so it is a trinomial.

Each term of the binomial multiplies each term of the trinomial, so 2 times 3 makes 6 products.

A grid keeps track: the binomial goes down the side, the trinomial across the top.

Start with x. x times x squared is x cubed, since the exponents add: 1 plus 2 is 3.

x times negative 3x is negative 3x squared.

x times 4 is 4x.

Then use the 2. 2 times x squared is 2x squared.

2 times negative 3x is negative 6x.

2 times 4 is 8.

Count them: 1, 2, 3, 4, 5, 6 products.

Missing one of the six is a common mistake. In a grid, a missing product leaves an empty box.

Now add the six products together.

Like terms have the same variable and the same power.

Negative 3x squared plus 2x squared is negative x squared, since negative 3 plus 2 is negative 1.

4x minus 6x is negative 2x, since 4 minus 6 is negative 2.

x cubed and 8 have no like terms, so the answer is x cubed minus x squared minus 2x plus 8.

Check with x equals 2. In the question, the brackets give 4 and 2, and 4 times 2 is 8.

The answer gives 8 minus 4 minus 4 plus 8, which is also 8.

Multiply every term by every term, then collect like terms.

Curriculum

Where this fits

British Columbia, Grade 10

Foundations of Mathematics and Pre Calculus 10, Algebra: multiplication of polynomial expressionsBC10-MA-29

Previous: Multiplying Two Binomials with an Area ModelNext: Squaring a Binomial: Don't Forget the Middle Term

The outcomes and strands follow the British Columbia curriculum.

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