Solve. Factor each expression. b.5y^{3}+135

Question
Polynomial factorization
Solve. Factor each expression.
b.$$5y^{3}+135$$

2021-01-09
Calculation:
Consider the polynomial as,
$$5y^{3}+135$$
First, take 5 as common factor,
$$5y^{3}+135=5(y)^{3}+5(27)$$
$$=5(y^{3}+3^{3})$$
According to the factorized form of sum of two cubes, $$u^{3}+v^{3}=(u+v)(u^{2}—uv+v^{2})$$.
$$5y^{3}+135=5(y+3)\left[y^{2}-y(3)+3^{2}\right]$$
$$=5(y+3)(y^{2}—3y+9)$$
Therefore, the factorization of the polynomial $$5y^{3}+135$$ is $$5(y + 3)(y^{2}—3y+9)$$.

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