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Question
Find the following product:
`(x/2 + 2y)(x^2/4 - xy + 4y^2)`
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Solution
`(x/2 + 2y)(x^2/4 - xy + 4y^2) = x/2(x^2/4 - xy + 4y^2) + 2y(x^2/4 - xy + 4y^2)`
= `x/2(x^2/4) + x/2(-xy) + x/2(4y)^2 + 2y(x^2/4) + 2y(-xy) + 2y(4y^2)`
= `x^3/8 - (x^2y)/2 + 2xy^2 + (x^2y)/2 - 2xy^2 + 8y^3`
= `x^3/8 + 8y^3`
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