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Factorise : x6 – 64y3 |
Answer» x6 – 64y3 = (x2)3 – 43y3 = (x2)3 – (4y)3 This is of the form a3 – b3 with a = x2, b = 4y a3 – b3 = (a – b)(a2 + ab + b2) (x2)3 – (4y)3 = (x2 – 4y) [(x2)2 + (x2)(4y) + (4y)2] = (x2 – 4y) [x4 + 4x2y + 16y2] ∴ x6 – 64y3 = (x2 – 4y) [x4 + 4x2y + 16y2] |
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