Solve (x+1)*2(x+2)(x-5)(x-4)

$$( x + 1 ) \cdot 2 ( x + 2 ) ( x - 5 ) ( x - 4 )$$

Evaluate

$$2\left(x-5\right)\left(x-4\right)\left(x+1\right)\left(x+2\right)$$

Solution Steps

Use the distributive property to multiply x+1 by 2.

$$\left(2x+2\right)\left(x+2\right)\left(x-5\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 2x+2 by each term of x+2.

$$\left(2x^{2}+4x+2x+4\right)\left(x-5\right)\left(x-4\right)$$

Combine 4x and 2x to get 6x.

$$\left(2x^{2}+6x+4\right)\left(x-5\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 2x^{2}+6x+4 by each term of x-5.

$$\left(2x^{3}-10x^{2}+6x^{2}-30x+4x-20\right)\left(x-4\right)$$

Combine -10x^{2} and 6x^{2} to get -4x^{2}.

$$\left(2x^{3}-4x^{2}-30x+4x-20\right)\left(x-4\right)$$

Combine -30x and 4x to get -26x.

$$\left(2x^{3}-4x^{2}-26x-20\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 2x^{3}-4x^{2}-26x-20 by each term of x-4.

$$2x^{4}-8x^{3}-4x^{3}+16x^{2}-26x^{2}+104x-20x+80$$

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

$$2x^{4}-12x^{3}+16x^{2}-26x^{2}+104x-20x+80$$

Combine 16x^{2} and -26x^{2} to get -10x^{2}.

$$2x^{4}-12x^{3}-10x^{2}+104x-20x+80$$

Combine 104x and -20x to get 84x.

$$2x^{4}-12x^{3}-10x^{2}+84x+80$$

Expand

$$2x^{4}-12x^{3}-10x^{2}+84x+80$$

Solution Steps

Use the distributive property to multiply x+1 by 2.

$$\left(2x+2\right)\left(x+2\right)\left(x-5\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 2x+2 by each term of x+2.

$$\left(2x^{2}+4x+2x+4\right)\left(x-5\right)\left(x-4\right)$$

Combine 4x and 2x to get 6x.

$$\left(2x^{2}+6x+4\right)\left(x-5\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 2x^{2}+6x+4 by each term of x-5.

$$\left(2x^{3}-10x^{2}+6x^{2}-30x+4x-20\right)\left(x-4\right)$$

Combine -10x^{2} and 6x^{2} to get -4x^{2}.

$$\left(2x^{3}-4x^{2}-30x+4x-20\right)\left(x-4\right)$$

Combine -30x and 4x to get -26x.

$$\left(2x^{3}-4x^{2}-26x-20\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of 2x^{3}-4x^{2}-26x-20 by each term of x-4.

$$2x^{4}-8x^{3}-4x^{3}+16x^{2}-26x^{2}+104x-20x+80$$

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

$$2x^{4}-12x^{3}+16x^{2}-26x^{2}+104x-20x+80$$

Combine 16x^{2} and -26x^{2} to get -10x^{2}.

$$2x^{4}-12x^{3}-10x^{2}+104x-20x+80$$

Combine 104x and -20x to get 84x.

$$2x^{4}-12x^{3}-10x^{2}+84x+80$$