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Find the product. Simplify your answer. $\newline$ $y^2(y^2 - 4y)$

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Multiply a polynomial by a monomial

Full solution

Q. Find the product. Simplify your answer.

\newline

y^2(y^2 - 4y)

Distribute $y^2$ : Distribute $y^2$ to both terms inside the parentheses. $\newline$ $y^2(y^2 - 4y) = y^2(y^2) - y^2(4y)$
Simplify $y^2(y^2)$ : Simplify $y^2(y^2)$ .
$y^2(y^2) = y^{(2+2)} = y^4$
Simplify $y^2(4y)$ : Simplify $y^2(4y)$ . $y^2(4y) = 4y^{2+1} = 4y^3$
Combine results: Combine the results from Step $2$ and Step $3$ . $y^2(y^2 - 4y) = y^4 - 4y^3$

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