Question

Factorise 27a^3 + 1/64b^3 + 27a^2/4b + 9a/16b^2

Answer 1

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Identity = (x+y) ³ = x³+y³+3xy(x+y)


$(3a {)}^{3} + \frac{1}{4b} {}^{3} + 3(3a)( \frac{1}{4b})(3a + \frac{1}{4b}) \\ \\ = (3a + \ \frac{1}{4b} {)}^{3} \\ \\ = ( 3a + \frac{1}{4b})(3a + \frac{1}{4b})(3a + \frac{1}{4b})$

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