Expressions · Grade 8

In Grade 8 you learn: collecting like terms and expressions with powers.

An algebraic expression uses letters to stand for numbers, like 3a + 2b. Simplifying it — collecting like terms and tidying products — makes it shorter and easier to work with, in the same way that 3 apples + 2 apples is 5 apples.

Key facts

• A term is a number, a letter, or numbers and letters multiplied together: 5, x, 3ab, 4x².
• Like terms have exactly the same letters and powers: 3x² and −x² are like terms; 3x² and 3x are not.
• Collect like terms by adding their coefficients; each term keeps the sign in front of it: 5a − 2b − a = 4a − 2b.
• A letter on its own has a coefficient of 1: x means 1x.
• Multiply terms by multiplying the numbers, then the letters: 3a × 4b = 12ab, and a × a × a = a³.
• Divide by cancelling numbers and letters: 12x²y ÷ 4xy = 3x.

Worked examples

Other years

• Expressions · Grade 7
• Expressions · Grade 9