Algebraic ManipulationAQA GCSE Maths: Flashcards

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What does the notation 'ab' mean in algebra?

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What does the notation 'ab' mean in algebra?: ab means a × b (a multiplied by b). In algebra, we omit the multiplication sign between variables and numbers.
Define 'like terms' in algebraic expressions.: Like terms are terms that have the same variable(s) raised to the same power(s). For example, 3x and 5x are like terms, but 3x and 3x² are not.
Simplify: 4a + 7b - 2a + 3b: 2a + 10b (Collect like terms: 4a - 2a = 2a and 7b + 3b = 10b)
Expand: 3(2x + 5): 6x + 15 (Multiply each term inside the bracket by 3)
What does it mean to factorise an expression?: Factorise means to write an expression as a product of its factors, usually by taking out the highest common factor (HCF) or grouping terms.
Factorise: x² + 7x + 12: (x + 3)(x + 4) (Find two numbers that multiply to give 12 and add to give 7)
Factorise: 2x² + 7x + 3: (2x + 1)(x + 3) (Use the AC method or trial and error for expressions of the form ax² + bx + c where a ≠ 1)
Complete the square for: x² + 6x + 5: (x + 3)² - 4 (Halve the coefficient of x to get 3, square it to get 9, then: (x + 3)² - 9 + 5 = (x + 3)² - 4)
Simplify: (6x²y) / (2xy): 3x (Cancel common factors: 6÷2 = 3, x²÷x = x, y÷y = 1)
What is the difference of two squares formula?: a² - b² = (a + b)(a - b) (This can be used to factorise expressions like x² - 9)
Factorise using the difference of two squares: x² - 25: (x + 5)(x - 5) (Recognise as x² - 5², so use a² - b² = (a + b)(a - b))
Rearrange the formula A = πr² to make r the subject.: r = √(A/π) (Divide both sides by π, then take the square root of both sides)
Rearrange v = u + at to make t the subject.: t = (v - u)/a (Subtract u from both sides, then divide by a)
Substitute a = 5, b = 3 into: 2ab + a²: 2(5)(3) + 5² = 30 + 25 = 55
Expand: (x + 2)(x + 3): x² + 5x + 6 (Use FOIL: x·x = x², x·3 + 2·x = 5x, 2·3 = 6)