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Lesson · Grade 9 · Mathematics

Multiplying a Polynomial by a Monomial

  • Grade 9
  • Mathematics
  • 2 min 13 s
  • British Columbia
  • BC9-MA-13

Using a rectangle 2n wide and n + 7 long, the video shows that 2n(n + 7) splits into two areas, 2n × n = 2n² and 2n × 7 = 14n, so 2n(n + 7) = 2n² + 14n: the distributive property, where the monomial multiplies every term in the bracket. It then shows the common mistake 2n² + 7 failing a check with n = 3 (25, not 60), works through 3x(x − 4) = 3x² − 12x, and ends on the recap: multiply the monomial by every term.

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In one sentence

The question this lesson answers

How do we multiply 2n by the bracket n plus 7?

2n is a monomial: a single term, the number 2 times the variable n.

Transcript

What the lesson says

How do we multiply 2n by the bracket n plus 7?

2n is a monomial: a single term, the number 2 times the variable n.

n plus 7 is a polynomial: terms added together. It has two terms.

Picture it as a rectangle, 2n wide and n plus 7 long.

Split the length into its two terms, n and 7. The rectangle splits in two.

The left part is 2n times n, which is 2n squared, since n times n is n squared.

The right part is 2n times 7, which is 14n, since 2 times 7 is 14.

Add the two parts. The whole area is 2n squared plus 14n.

2n squared and 14n are not like terms. Like terms have the same variable and the same power.

This is the distributive property: 2n multiplies the first term, then the second term.

A common mistake is to multiply only the first term and write 2n squared plus 7.

Check with n equals 3. 2n is 6 and n plus 7 is 10, so 6 times 10 is 60.

Our answer: 2 times 3 squared is 18, and 14 times 3 is 42. 18 plus 42 is 60 again.

The mistake gives 18 plus 7, which is 25, not 60.

The same works with a minus sign: 3x times the bracket x minus 4.

3x times x is 3x squared, and 3x times negative 4 is negative 12x.

So the answer is 3x squared minus 12x.

To multiply a polynomial by a monomial, multiply the monomial by every term in the polynomial.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Patterns and algebra: operations with polynomials, of degree less than or equal to 2BC9-MA-13

Previous: Subtracting Polynomials: Change Every Sign in the Second BracketNext: Dividing a Polynomial by a Monomial

The outcomes and strands follow the British Columbia curriculum.

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