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

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Multiply a polynomial by a monomial

Full solution

Q. Find the product. Simplify your answer.

\newline

f^2(-f^2 + 4)

Distribute $f^2$ : $f^2(-f^2 + 4)$ $\newline$ Distribute $f^2$ to both $-f^2$ and $+4$ . $\newline$ $f^2(-f^2 + 4) = f^2(-f^2) + f^2(4)$
Simplify $f^2(-f^2)$ : Simplify $f^2(-f^2)$ .
$f^2(-f^2)$
$= f^2 \cdot -f^2$
$= -f^{2+2}$
$= -f^4$
Simplify $f^2(4)$ : Simplify $f^2(4)$ .
$f^2(4)$
= $4 \times f^2$
= $4f^2$
Combine results: Combine the results from Step $2$ and Step $3$ . $\newline$ We found: $\newline$ $f^2(-f^2) = -f^4$ $\newline$ $f^2(4) = 4f^2$ $\newline$ So, $f^2(-f^2 + 4) = -f^4 + 4f^2$

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