Solve 4x^2(2x^2-2)+2x^2(4x+3)-3x(4x^2+1)=

$$4 x ^ { 2 } ( 2 x ^ { 2 } - 2 ) + 2 x ^ { 2 } ( 4 x + 3 ) - 3 x ( 4 x ^ { 2 } + 1 ) =$$

Evaluate

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

Solution Steps

Use the distributive property to multiply 4x^{2} by 2x^{2}-2.

$$8x^{4}-8x^{2}+2x^{2}\left(4x+3\right)-3x\left(4x^{2}+1\right)$$

Use the distributive property to multiply 2x^{2} by 4x+3.

$$8x^{4}-8x^{2}+8x^{3}+6x^{2}-3x\left(4x^{2}+1\right)$$

Combine -8x^{2} and 6x^{2} to get -2x^{2}.

$$8x^{4}-2x^{2}+8x^{3}-3x\left(4x^{2}+1\right)$$

Use the distributive property to multiply -3x by 4x^{2}+1.

$$8x^{4}-2x^{2}+8x^{3}-12x^{3}-3x$$

Combine 8x^{3} and -12x^{3} to get -4x^{3}.

$$8x^{4}-2x^{2}-4x^{3}-3x$$

Expand

$$8x^{4}-4x^{3}-2x^{2}-3x$$

Solution Steps

Use the distributive property to multiply 4x^{2} by 2x^{2}-2.

$$8x^{4}-8x^{2}+2x^{2}\left(4x+3\right)-3x\left(4x^{2}+1\right)$$

Use the distributive property to multiply 2x^{2} by 4x+3.

$$8x^{4}-8x^{2}+8x^{3}+6x^{2}-3x\left(4x^{2}+1\right)$$

Combine -8x^{2} and 6x^{2} to get -2x^{2}.

$$8x^{4}-2x^{2}+8x^{3}-3x\left(4x^{2}+1\right)$$

Use the distributive property to multiply -3x by 4x^{2}+1.

$$8x^{4}-2x^{2}+8x^{3}-12x^{3}-3x$$

Combine 8x^{3} and -12x^{3} to get -4x^{3}.

$$8x^{4}-2x^{2}-4x^{3}-3x$$