Rechenkiste

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Calculating · typical for Grades 7 and 8

Algebraic expressions – worksheets to print

Calculate with variables: collect like terms, substitute values, multiply out and factor out brackets, write expressions for situations and use the binomial formulas.

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Create a worksheet: Algebraic expressions How it works: explanations & examples
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Algebraic expressions: explained simply

An expression (term) is a calculation made of numbers and letters, for example 3x + 5. The letter stands for a number that is unknown or may change.

How to work it out

  • Collecting: only like terms (the same letters with the same powers) can be combined: 3x + 5 − x + 2 = 2x + 7.
  • Expanding: the factor in front of the bracket is multiplied by every term inside: 3 · (x + 4) = 3x + 12. Factoring out is the reverse: 6x + 12 = 6 · (x + 2).
  • Substituting: replace every letter by its value, put negative values in brackets and follow the order of operations.

An example, step by step

Simplify: 3x + 5 − x + 2

  1. Sort into like terms: the x terms are 3x and −x, the numbers are 5 and 2.
  2. 3x − x = 2x and 5 + 2 = 7.
  3. Answer: 2x + 7.

Understand other variations

Two brackets

(x + 3)(x + 5): multiply every term of the first bracket by every term of the second: x · x + x · 5 + 3 · x + 3 · 5 = x² + 8x + 15.

Binomial formulas

(a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b² and (a + b)(a − b) = a² − b². Example: (x + 3)² = x² + 6x + 9.

Writing an expression

A notebook costs x €, a pen 2 €: 3 notebooks and 2 pens cost 3x + 4 €.

Substituting negative values

3x − 5 for x = −2: 3 · (−2) − 5 = −6 − 5 = −11.

Your turn

Expand and simplify: 2 · (x + 3) + 4x

Show the answer and method

2x + 6 + 4x = 6x + 6. Check with x = 1: 2 · 4 + 4 = 12 and 6 + 6 = 12.

Ready-made worksheets: Algebraic expressions

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Grade 7 · SingleCollecting like termsLike terms, also with minus signs and two variables
Use
Grade 9 · SingleBinomial formulas(a + b)², (a − b)² and (a + b)(a − b)
Use
Grade 8 · MixedExpressions & functionsFactorising, simplifying expressions, linear functions
Use

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