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Question
Factorize the following expressions:
`8x^2y^3 - x^5`
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Solution
`=x^2(8y^3 - x^3)`
`= x^2((2y)^3 - x^3)`
`= x^2(2y - x)((2y)^2 + 2y(x) + x^2) [∵ a^3 - b^3 = (a - b)(a^2 + ab + b^2)]`
`= x^2(2y - x)((2y)^2 + 2y(x)+ x^2)` `[∵ a^3 - b^3 = (a - b)(a^2 + ab + b^2)]`
`= x^2(2y - x)(4y^2 + 2xy + x^2)`
`∴ 8x^2y^3 - x^5 = x^2(2y - x)(4y^2 + 2xy + x^2)`
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