factor:
x³+27y³
by the sum of two cubes
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Answer:
To factor the expression \(x^3 + 27y^3\) by the sum of two cubes, we use the following formula:
\[a^3 + b^3 = (a + b)(a^2 - ab + b^2)\]
In this case, we have \(x^3 + 27y^3\). Comparing this with the formula, we see that \(a = x\) and \(b = 3y\). Substituting these values, we get:
\[x^3 + 27y^3 = (x + 3y)(x^2 - 3xy + 9y^2)\]
Therefore, the factored form of \(x^3 + 27y^3\) by the sum of two cubes is \((x + 3y)(x^2 - 3xy + 9y^2)\).