Solve (8x^3-2x^2-x)(3x^2-8)+(x^3-8x)(4x+1)(4x-1)+(8{x}^2-4x)

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

Evaluate

$$2x\left(20x^{4}-3x^{3}-98x^{2}+12x+6\right)$$

Solution Steps

Use the distributive property to multiply 8x^{3}-2x^{2}-x by 3x^{2}-8 and combine like terms.

$$24x^{5}-67x^{3}-6x^{4}+16x^{2}+8x+\left(x^{3}-8x\right)\left(4x+1\right)\left(4x-1\right)+8x^{2}-4x$$

Use the distributive property to multiply x^{3}-8x by 4x+1.

$$24x^{5}-67x^{3}-6x^{4}+16x^{2}+8x+\left(4x^{4}+x^{3}-32x^{2}-8x\right)\left(4x-1\right)+8x^{2}-4x$$

Use the distributive property to multiply 4x^{4}+x^{3}-32x^{2}-8x by 4x-1 and combine like terms.

$$24x^{5}-67x^{3}-6x^{4}+16x^{2}+8x+16x^{5}-129x^{3}+8x+8x^{2}-4x$$

Combine 24x^{5} and 16x^{5} to get 40x^{5}.

$$40x^{5}-67x^{3}-6x^{4}+16x^{2}+8x-129x^{3}+8x+8x^{2}-4x$$

Combine -67x^{3} and -129x^{3} to get -196x^{3}.

$$40x^{5}-196x^{3}-6x^{4}+16x^{2}+8x+8x+8x^{2}-4x$$

Combine 8x and 8x to get 16x.

$$40x^{5}-196x^{3}-6x^{4}+16x^{2}+16x+8x^{2}-4x$$

Combine 16x^{2} and 8x^{2} to get 24x^{2}.

$$40x^{5}-196x^{3}-6x^{4}+24x^{2}+16x-4x$$

Combine 16x and -4x to get 12x.

$$40x^{5}-196x^{3}-6x^{4}+24x^{2}+12x$$

Expand

$$40x^{5}-6x^{4}-196x^{3}+24x^{2}+12x$$

Solution Steps

Use the distributive property to multiply 8x^{3}-2x^{2}-x by 3x^{2}-8 and combine like terms.

$$24x^{5}-67x^{3}-6x^{4}+16x^{2}+8x+\left(x^{3}-8x\right)\left(4x+1\right)\left(4x-1\right)+8x^{2}-4x$$

Use the distributive property to multiply x^{3}-8x by 4x+1.

$$24x^{5}-67x^{3}-6x^{4}+16x^{2}+8x+\left(4x^{4}+x^{3}-32x^{2}-8x\right)\left(4x-1\right)+8x^{2}-4x$$

Use the distributive property to multiply 4x^{4}+x^{3}-32x^{2}-8x by 4x-1 and combine like terms.

$$24x^{5}-67x^{3}-6x^{4}+16x^{2}+8x+16x^{5}-129x^{3}+8x+8x^{2}-4x$$

Combine 24x^{5} and 16x^{5} to get 40x^{5}.

$$40x^{5}-67x^{3}-6x^{4}+16x^{2}+8x-129x^{3}+8x+8x^{2}-4x$$

Combine -67x^{3} and -129x^{3} to get -196x^{3}.

$$40x^{5}-196x^{3}-6x^{4}+16x^{2}+8x+8x+8x^{2}-4x$$

Combine 8x and 8x to get 16x.

$$40x^{5}-196x^{3}-6x^{4}+16x^{2}+16x+8x^{2}-4x$$

Combine 16x^{2} and 8x^{2} to get 24x^{2}.

$$40x^{5}-196x^{3}-6x^{4}+24x^{2}+16x-4x$$

Combine 16x and -4x to get 12x.

$$40x^{5}-196x^{3}-6x^{4}+24x^{2}+12x$$