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Factorize: 8/(27)x^3+1+4/3x^2+2x...

Factorize: `8/(27)x^3+1+4/3x^2+2x`

Text Solution

Verified by Experts

Given expression
`(8/(27)x^3+1+4/3x^2+2x)`
= `(2/3 x)^3 + (1)^3 + 3 ×(2/3 x)^2 × 1 + 3(1)^2 × (2/3 x)`
= `(2/3 x + 1)^3 [ Since, a^3 + b^3 + 3a^2b + 3ab^2 = (a + b)^3]`
=`(2/3x + 1)(2/3x + 1)(2/3x + 1)`
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