Solve left(x+5right)left(x+2right)left(x-1right)(x-4)(x-7)=

$$\left( x+5 \right) \left( x+2 \right) \left( x-1 \right) (x-4)(x-7)=$$

Evaluate

$$\left(x-7\right)\left(x-4\right)\left(x-1\right)\left(x+2\right)\left(x+5\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x+5 by each term of x+2.

$$\left(x^{2}+2x+5x+10\right)\left(x-1\right)\left(x-4\right)\left(x-7\right)$$

Combine 2x and 5x to get 7x.

$$\left(x^{2}+7x+10\right)\left(x-1\right)\left(x-4\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of x^{2}+7x+10 by each term of x-1.

$$\left(x^{3}-x^{2}+7x^{2}-7x+10x-10\right)\left(x-4\right)\left(x-7\right)$$

Combine -x^{2} and 7x^{2} to get 6x^{2}.

$$\left(x^{3}+6x^{2}-7x+10x-10\right)\left(x-4\right)\left(x-7\right)$$

Combine -7x and 10x to get 3x.

$$\left(x^{3}+6x^{2}+3x-10\right)\left(x-4\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of x^{3}+6x^{2}+3x-10 by each term of x-4.

$$\left(x^{4}-4x^{3}+6x^{3}-24x^{2}+3x^{2}-12x-10x+40\right)\left(x-7\right)$$

Combine -4x^{3} and 6x^{3} to get 2x^{3}.

$$\left(x^{4}+2x^{3}-24x^{2}+3x^{2}-12x-10x+40\right)\left(x-7\right)$$

Combine -24x^{2} and 3x^{2} to get -21x^{2}.

$$\left(x^{4}+2x^{3}-21x^{2}-12x-10x+40\right)\left(x-7\right)$$

Combine -12x and -10x to get -22x.

$$\left(x^{4}+2x^{3}-21x^{2}-22x+40\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of x^{4}+2x^{3}-21x^{2}-22x+40 by each term of x-7.

$$x^{5}-7x^{4}+2x^{4}-14x^{3}-21x^{3}+147x^{2}-22x^{2}+154x+40x-280$$

Combine -7x^{4} and 2x^{4} to get -5x^{4}.

$$x^{5}-5x^{4}-14x^{3}-21x^{3}+147x^{2}-22x^{2}+154x+40x-280$$

Combine -14x^{3} and -21x^{3} to get -35x^{3}.

$$x^{5}-5x^{4}-35x^{3}+147x^{2}-22x^{2}+154x+40x-280$$

Combine 147x^{2} and -22x^{2} to get 125x^{2}.

$$x^{5}-5x^{4}-35x^{3}+125x^{2}+154x+40x-280$$

Combine 154x and 40x to get 194x.

$$x^{5}-5x^{4}-35x^{3}+125x^{2}+194x-280$$

Expand

$$x^{5}-5x^{4}-35x^{3}+125x^{2}+194x-280$$

Solution Steps

Apply the distributive property by multiplying each term of x+5 by each term of x+2.

$$\left(x^{2}+2x+5x+10\right)\left(x-1\right)\left(x-4\right)\left(x-7\right)$$

Combine 2x and 5x to get 7x.

$$\left(x^{2}+7x+10\right)\left(x-1\right)\left(x-4\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of x^{2}+7x+10 by each term of x-1.

$$\left(x^{3}-x^{2}+7x^{2}-7x+10x-10\right)\left(x-4\right)\left(x-7\right)$$

Combine -x^{2} and 7x^{2} to get 6x^{2}.

$$\left(x^{3}+6x^{2}-7x+10x-10\right)\left(x-4\right)\left(x-7\right)$$

Combine -7x and 10x to get 3x.

$$\left(x^{3}+6x^{2}+3x-10\right)\left(x-4\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of x^{3}+6x^{2}+3x-10 by each term of x-4.

$$\left(x^{4}-4x^{3}+6x^{3}-24x^{2}+3x^{2}-12x-10x+40\right)\left(x-7\right)$$

Combine -4x^{3} and 6x^{3} to get 2x^{3}.

$$\left(x^{4}+2x^{3}-24x^{2}+3x^{2}-12x-10x+40\right)\left(x-7\right)$$

Combine -24x^{2} and 3x^{2} to get -21x^{2}.

$$\left(x^{4}+2x^{3}-21x^{2}-12x-10x+40\right)\left(x-7\right)$$

Combine -12x and -10x to get -22x.

$$\left(x^{4}+2x^{3}-21x^{2}-22x+40\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of x^{4}+2x^{3}-21x^{2}-22x+40 by each term of x-7.

$$x^{5}-7x^{4}+2x^{4}-14x^{3}-21x^{3}+147x^{2}-22x^{2}+154x+40x-280$$

Combine -7x^{4} and 2x^{4} to get -5x^{4}.

$$x^{5}-5x^{4}-14x^{3}-21x^{3}+147x^{2}-22x^{2}+154x+40x-280$$

Combine -14x^{3} and -21x^{3} to get -35x^{3}.

$$x^{5}-5x^{4}-35x^{3}+147x^{2}-22x^{2}+154x+40x-280$$

Combine 147x^{2} and -22x^{2} to get 125x^{2}.

$$x^{5}-5x^{4}-35x^{3}+125x^{2}+154x+40x-280$$

Combine 154x and 40x to get 194x.

$$x^{5}-5x^{4}-35x^{3}+125x^{2}+194x-280$$