KnowledgeMadeFun, home

Lesson · Grade 9 · Mathematics

Subtracting Polynomials: Change Every Sign in the Second Bracket

  • Grade 9
  • Mathematics
  • 2 min 6 s
  • British Columbia
  • BC9-MA-12

Algebra tiles model (5x − 7) − (2x + 3). The second set of tiles flips colour to show that subtracting means adding the opposite, and the same step is written in symbols as 5x − 7 − 2x − 3. Like terms are then collected with zero pairs to give 3x − 10. The video also shows the common mistake of changing only the first sign, which gives 3x − 4, and a check with x = 4 confirms that 3x − 10 matches and 3x − 4 does not.

Anyone can watch two lessons on the website without an account. Signing in is free, no payment and no card, and opens three a day; Plus has no limit.

Loading

Share to Google Classroom

In one sentence

The question this lesson answers

How do we subtract 2x plus 3 from 5x minus 7?

A polynomial is made of terms, the parts joined by plus or minus signs. Each term keeps its sign: 5x, negative 7, 2x and plus 3.

Transcript

What the lesson says

How do we subtract 2x plus 3 from 5x minus 7?

A polynomial is made of terms, the parts joined by plus or minus signs. Each term keeps its sign: 5x, negative 7, 2x and plus 3.

In algebra tiles, a long tile stands for x and a small unit tile stands for 1. Blue tiles are positive, pink tiles are negative.

Five positive x tiles and seven negative unit tiles make 5x minus 7.

Two positive x tiles and three positive unit tiles make 2x plus 3.

Subtracting means adding the opposite, with every sign changed. So every tile in the second bracket flips colour, giving negative 2x minus 3.

In symbols, change every sign in the second bracket: 5x minus 7 minus 2x minus 3.

Now collect like terms, the terms with the same variable and the same power.

A positive and a negative x tile make a zero pair, worth 0, so 5x minus 2x is 3x.

The unit tiles are all negative: negative 7 minus 3 is negative 10.

So the answer is 3x minus 10.

A common mistake is changing only the first sign: 5x minus 7 minus 2x plus 3, which gives 3x minus 4.

Check with x equal to 4. The question becomes 20 minus 7, take away 8 plus 3, which is 13 minus 11, or 2.

Our answer gives 12 minus 10, also 2. The wrong one gives 12 minus 4, which is 8, not 2.

To subtract a polynomial, change the sign of every term in the second bracket, then collect like terms.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Patterns and algebra: operations with polynomials, of degree less than or equal to 2BC9-MA-12

Previous: Adding Polynomials by Collecting Like TermsNext: Multiplying a Polynomial by a Monomial

The outcomes and strands follow the British Columbia curriculum.

Keep going

More on this topic