Find the Product f(x)=-x^2 , g(x)=4x-1

$f (x) = - x^{2}$ , $g (x) = 4 x - 1$

Replace the function designators with the actual functions in $f (x) \cdot (g (x))$ .

$(- x^{2}) \cdot (4 x - 1)$

Simplify.

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Apply the distributive property.

$- x^{2} (4 x) - x^{2} \cdot - 1$

Rewrite using the commutative property of multiplication.

$- 1 \cdot 4 (x^{2} x) - x^{2} \cdot - 1$

Multiply $- x^{2} \cdot - 1$ .

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Multiply $- 1$ by $- 1$ .

$- 1 \cdot 4 (x^{2} x) + 1 x^{2}$

Multiply $x^{2}$ by $1$ .

$- 1 \cdot 4 (x^{2} x) + x^{2}$

Simplify each term.

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Multiply $x^{2}$ by $x$ by adding the exponents.

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Multiply $x^{2}$ by $x$ .

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Raise $x$ to the power of $1$ .

$- 1 \cdot 4 (x^{2} x^{1}) + x^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 1 \cdot 4 x^{2 + 1} + x^{2}$

Add $2$ and $1$ .

$- 1 \cdot 4 x^{3} + x^{2}$

Multiply $- 1$ by $4$ .

$- 4 x^{3} + x^{2}$

Find the Product f(x)=-x^2 , g(x)=4x-1

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