Solve (4z^2+7z-8)(-z+3)

$$( 4 z ^ { 2 } + 7 z - 8 ) ( - z + 3 )$$

Evaluate

$$\left(3-z\right)\left(4z^{2}+7z-8\right)$$

Solution Steps

Use the distributive property to multiply 4z^{2}+7z-8 by -z+3.

$$4z^{2}\left(-z\right)+12z^{2}+7z\left(-z\right)+21z-8\left(-z\right)-24$$

Multiply -8 and -1 to get 8.

$$4z^{2}\left(-z\right)+12z^{2}+7z\left(-z\right)+21z+8z-24$$

Combine 21z and 8z to get 29z.

$$4z^{2}\left(-z\right)+12z^{2}+7z\left(-z\right)+29z-24$$

Multiply 4 and -1 to get -4.

$$-4z^{2}z+12z^{2}+7z\left(-1\right)z+29z-24$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-4z^{3}+12z^{2}+7z\left(-1\right)z+29z-24$$

Multiply z and z to get z^{2}.

$$-4z^{3}+12z^{2}+7z^{2}\left(-1\right)+29z-24$$

Multiply 7 and -1 to get -7.

$$-4z^{3}+12z^{2}-7z^{2}+29z-24$$

Combine 12z^{2} and -7z^{2} to get 5z^{2}.

$$-4z^{3}+5z^{2}+29z-24$$

Expand

$$-4z^{3}+5z^{2}+29z-24$$

Solution Steps

Use the distributive property to multiply 4z^{2}+7z-8 by -z+3.

$$4z^{2}\left(-z\right)+12z^{2}+7z\left(-z\right)+21z-8\left(-z\right)-24$$

Multiply -8 and -1 to get 8.

$$4z^{2}\left(-z\right)+12z^{2}+7z\left(-z\right)+21z+8z-24$$

Combine 21z and 8z to get 29z.

$$4z^{2}\left(-z\right)+12z^{2}+7z\left(-z\right)+29z-24$$

Multiply 4 and -1 to get -4.

$$-4z^{2}z+12z^{2}+7z\left(-1\right)z+29z-24$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-4z^{3}+12z^{2}+7z\left(-1\right)z+29z-24$$

Multiply z and z to get z^{2}.

$$-4z^{3}+12z^{2}+7z^{2}\left(-1\right)+29z-24$$

Multiply 7 and -1 to get -7.

$$-4z^{3}+12z^{2}-7z^{2}+29z-24$$

Combine 12z^{2} and -7z^{2} to get 5z^{2}.

$$-4z^{3}+5z^{2}+29z-24$$