Solve 3left(4x^3+3x^2+x-8right)^2-8

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

Expand

$$48x^{6}+72x^{5}+51x^{4}-174x^{3}-141x^{2}-48x+184$$

Solution Steps

Square 4x^{3}+3x^{2}+x-8.

$$3\left(16x^{6}+24x^{5}+17x^{4}-58x^{3}-47x^{2}-16x+64\right)-8$$

Use the distributive property to multiply 3 by 16x^{6}+24x^{5}+17x^{4}-58x^{3}-47x^{2}-16x+64.

$$48x^{6}+72x^{5}+51x^{4}-174x^{3}-141x^{2}-48x+192-8$$

Subtract 8 from 192 to get 184.

$$48x^{6}+72x^{5}+51x^{4}-174x^{3}-141x^{2}-48x+184$$

Evaluate

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

Solution Steps

Square 4x^{3}+3x^{2}+x-8.

$$3\left(16x^{6}+24x^{5}+17x^{4}-58x^{3}-47x^{2}-16x+64\right)-8$$

Use the distributive property to multiply 3 by 16x^{6}+24x^{5}+17x^{4}-58x^{3}-47x^{2}-16x+64.

$$48x^{6}+72x^{5}+51x^{4}-174x^{3}-141x^{2}-48x+192-8$$

Subtract 8 from 192 to get 184.

$$48x^{6}+72x^{5}+51x^{4}-174x^{3}-141x^{2}-48x+184$$