Solve (z^4-7z^3)(6z^3+5z^2-5z)(6{z}^2-6z-3)

$$( { z }^{ 4 } -7 { z }^{ 3 } )(6 { z }^{ 3 } +5 { z }^{ 2 } -5z)(6 { z }^{ 2 } -6z-3)$$

Evaluate

$$3\left(z-7\right)\left(2z^{2}-2z-1\right)\left(6z^{2}+5z-5\right)z^{4}$$

Solution Steps

Use the distributive property to multiply z^{4}-7z^{3} by 6z^{3}+5z^{2}-5z and combine like terms.

$$\left(6z^{7}-37z^{6}-40z^{5}+35z^{4}\right)\left(6z^{2}-6z-3\right)$$

Use the distributive property to multiply 6z^{7}-37z^{6}-40z^{5}+35z^{4} by 6z^{2}-6z-3 and combine like terms.

$$36z^{9}-258z^{8}-36z^{7}+561z^{6}-90z^{5}-105z^{4}$$

Expand

$$36z^{9}-258z^{8}-36z^{7}+561z^{6}-90z^{5}-105z^{4}$$

Solution Steps

Use the distributive property to multiply z^{4}-7z^{3} by 6z^{3}+5z^{2}-5z and combine like terms.

$$\left(6z^{7}-37z^{6}-40z^{5}+35z^{4}\right)\left(6z^{2}-6z-3\right)$$

Use the distributive property to multiply 6z^{7}-37z^{6}-40z^{5}+35z^{4} by 6z^{2}-6z-3 and combine like terms.

$$36z^{9}-258z^{8}-36z^{7}+561z^{6}-90z^{5}-105z^{4}$$