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At GCSE you extend algebraic manipulation to include triple-bracket expansion, all forms of factorisation, algebraic fractions and completing the square.
(2x + 3)(x − 5) = 2x² − 10x + 3x − 15 = 2x² − 7x − 15
Expand two brackets first, then multiply the result by the third.
Example: (x + 2)(x − 1)(x + 3) Step 1: (x + 2)(x − 1) = x² + x − 2 Step 2: (x² + x − 2)(x + 3) = x³ + 3x² + x² + 3x − 2x − 6 = x³ + 4x² + x − 6
12x³y − 8x²y² = 4x²y(3x − 2y)
a² − b² = (a + b)(a − b)
9x² − 25 = (3x + 5)(3x − 5) 16 − x² = (4 + x)(4 − x)
Find two numbers that multiply to c and add to b.
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