Equivalent Expressions Worksheets
Free printable equivalent expressions worksheets: expand brackets, combine like terms and factor, all on one sheet. With an answer key.
One sheet with all three ways of rewriting an expression: expand a bracket, 2(3x + 5) = 6x + 10; combine like terms, 4x + 7 - x + 2 = 3x + 9; and factor, 8x + 12 = 4(2x + 3). Every page has the three in equal numbers - six of each on an 18-problem sheet.
The shape of each question says which move it needs. A bracket means multiply it out, four terms mean collect them, and a factoring question has a bracket drawn in its blank, ____(________), for the factor to go in front of. Every answer is written with the x term first.
What this worksheet covers
- Expand, simplify and factor linear expressions
- Choose the right rewrite from the shape of an expression
Common Core standards
- 6.EE.A.3 Apply the properties of operations to generate equivalent expressions.
- 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor and expand linear expressions.
Frequently asked questions
Why mix the three?
Because a student has to choose. On a page of only one kind the move is decided before the question is read; here they have to look at the expression and decide whether to expand it, simplify it or factor it.
What does equivalent mean?
Equal for every value of x. 2(3x + 5) and 6x + 10 give the same number whatever x is - try x = 1, and both make 16. Rewriting an expression changes how it looks, never what it is worth.
Are answers other than the key's right?
Any expression equal to the key's is, such as 10 + 6x for 6x + 10. Factoring is the one to watch: 2(4x + 6) equals 8x + 12 but is not finished, because the key takes out the greatest common factor.
What grade is this?
Sixth and seventh. Sixth grade writes equivalent expressions with the distributive property; seventh grade adds, subtracts, factors and expands them with negative numbers, which are one setting away under Advanced options.