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Question
Factorise:
64a3 + 125b3
Sum
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Solution
To factorise, 64a3 + 125b3
Compare the expression with the algebraic identity a3 + b3 = (a + b)(a2 – ab + b2)
We know that,
64 = 43
125 = 53
So, 64a3 + 125b3 = (4a)3 + (5b)3
Therefore, a = 4a, b = 5b
Hence, 64a3 + 125b3 = (4a + 5b) (16a2 – 20ab + 25b2)
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