Solve (x-3)(2x^2-5x+4)-2x(x^2-8x+1)

$$( x - 3 ) ( 2 x ^ { 2 } - 5 x + 4 ) - 2 x ( x ^ { 2 } - 8 x + 1 )$$

Evaluate

$$\left(5x-3\right)\left(x+4\right)$$

Solution Steps

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

$$2x^{3}-11x^{2}+19x-12-2x\left(x^{2}-8x+1\right)$$

Use the distributive property to multiply -2x by x^{2}-8x+1.

$$2x^{3}-11x^{2}+19x-12-2x^{3}+16x^{2}-2x$$

Combine 2x^{3} and -2x^{3} to get 0.

$$-11x^{2}+19x-12+16x^{2}-2x$$

Combine -11x^{2} and 16x^{2} to get 5x^{2}.

$$5x^{2}+19x-12-2x$$

Combine 19x and -2x to get 17x.

$$5x^{2}+17x-12$$

Expand

$$5x^{2}+17x-12$$

Solution Steps

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

$$2x^{3}-11x^{2}+19x-12-2x\left(x^{2}-8x+1\right)$$

Use the distributive property to multiply -2x by x^{2}-8x+1.

$$2x^{3}-11x^{2}+19x-12-2x^{3}+16x^{2}-2x$$

Combine 2x^{3} and -2x^{3} to get 0.

$$-11x^{2}+19x-12+16x^{2}-2x$$

Combine -11x^{2} and 16x^{2} to get 5x^{2}.

$$5x^{2}+19x-12-2x$$

Combine 19x and -2x to get 17x.

$$5x^{2}+17x-12$$