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Algebraic expressions – practice for Years 8–9

Sample questions on Algebraic expressions with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 8–9
Curriculum area
Number and algebra

Question types: Simplifying an expression

Rule: Algebraic expressions

(a + b)² = a² + 2ab + b², (a − b)² = a² − 2ab + b², (a + b)(a − b) = a² − b²

After expanding, collect like terms: x² with x², x with x, numbers with numbers.

Example: (x + 3)² − (x − 3)(x + 3) = x² + 6x + 9 − (x² − 9) = 6x + 18

Watch out: (x + 3)² is not x² + 9. And a minus in front of a bracket changes the signs of all the terms in it.

Sample questions

  1. Question 1 Easy

    Simplify the expression: (x + 1)² − (x − 1)(x + 1)

    Show the solution
    Answer: 2x + 2

    How it works: (x + 1)² = x² + 2x + 1; (x − 1)(x + 1) = x² − 1; the difference is 2x + 2

  2. Question 2 Normal

    Simplify the expression: (x + 2)² − (x − 1)(x + 1)

    Show the solution
    Answer: 4x + 5

    How it works: (x + 2)² = x² + 4x + 4; (x − 1)(x + 1) = x² − 1; the difference is 4x + 5

  3. Question 3 Hard

    Simplify the expression: (x + 2)² − (x − 3)(x + 3)

    Show the solution
    Answer: 4x + 13

    How it works: (x + 2)² = x² + 4x + 4; (x − 3)(x + 3) = x² − 9; the difference is 4x + 13

Related topics

All Maths topics

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