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Question
Factorise: 75(x + y)2 - 48(x - y)2
Sum
Solution
75(x + y)2 - 48(x - y)2
= 3[25 (x + y)2 - 16 (x - y)2]
= 3[{5 (x + y)2} - {4 (x - y)}2]
Using a2 – b2 = (a + b) (a – b)
= 3 [5(x + y) + 4(x - y)] [5(x + y) - 4(x - y)]
= 3 [5x + 5y + 4x - 4y] [5x + 5y - 4x + 4y]
= 3 (9x + y) (x + 9y)
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Factorisation by Difference of Two Squares
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