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Question
Factorize `8/27 x^3 + 1 + 4/3 x^2 + 2x`
Solution
`= (2/3 x)^3 + (1)^3 + 3 xx (2/3 x)^2 xx 1 + 3(1)^2 xx (2/3 x)`
`= (2/3 x + 1)^3 [∵ a^3 + b^3 + 3a^2b + 3ab^2 = (a + b)^2]`
`= (2/3 x + 1)(2/3x + 1)(2/3x + 1)`
`∴ 8/27 x^3 + 1 + 4/3 x^2 + 2x = (2/3x + 1)(2/3 x + 1)(2/3x + 1)`
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