GCSE Maths · Topic guide
Simplifying Algebra
Simplifying an algebraic expression means writing it as concisely as possible by collecting like terms - terms with exactly the same letters and powers - and tidying up multiplication and division of terms.
Method
- Identify like terms: terms that have the same letter(s) raised to the same power, e.g. 3x and 5x, or 2x^2 and -x^2.
- Add or subtract the numbers (coefficients) in front of like terms, keeping the letter part unchanged.
- Terms that are not alike, such as x and x^2, or x and y, cannot be combined and stay separate.
- When multiplying terms, multiply the numbers together and multiply the letters together, adding indices for the same letter (e.g. 2a x 3a = 6a^2).
- When dividing terms, divide the numbers and subtract indices for the same letter (e.g. 8a^3 divided by 2a = 4a^2).
Worked example
Simplify 5x + 3y - 2x + 4y - x^2.
- Group the like terms together: (5x - 2x) + (3y + 4y) - x^2.
- Combine the x terms: 5x - 2x = 3x.
- Combine the y terms: 3y + 4y = 7y.
- The x^2 term has no other like term, so it stays as it is.
- Final simplified answer: 3x + 7y - x^2.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE exam paper, with a full mark scheme.
Q1[2 marks]
Simplify fully: 6x + 3y - 2x - 8y + x^2.
Q2[3 marks]
A triangle has sides given by the expressions 2a + 3b, a + 5b and 3a - b. Write an expression for its perimeter in its simplest form.
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