Solve (2x-3)(x+5)(x+1)(x-4)(x-7)

$$(2x-3)(x+5)(x+1)(x-4)(x-7)$$

Evaluate

$$\left(x-7\right)\left(x-4\right)\left(2x-3\right)\left(x+1\right)\left(x+5\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-3 by each term of x+5.

$$\left(2x^{2}+10x-3x-15\right)\left(x+1\right)\left(x-4\right)\left(x-7\right)$$

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

$$\left(2x^{2}+7x-15\right)\left(x+1\right)\left(x-4\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of 2x^{2}+7x-15 by each term of x+1.

$$\left(2x^{3}+2x^{2}+7x^{2}+7x-15x-15\right)\left(x-4\right)\left(x-7\right)$$

Combine 2x^{2} and 7x^{2} to get 9x^{2}.

$$\left(2x^{3}+9x^{2}+7x-15x-15\right)\left(x-4\right)\left(x-7\right)$$

Combine 7x and -15x to get -8x.

$$\left(2x^{3}+9x^{2}-8x-15\right)\left(x-4\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of 2x^{3}+9x^{2}-8x-15 by each term of x-4.

$$\left(2x^{4}-8x^{3}+9x^{3}-36x^{2}-8x^{2}+32x-15x+60\right)\left(x-7\right)$$

Combine -8x^{3} and 9x^{3} to get x^{3}.

$$\left(2x^{4}+x^{3}-36x^{2}-8x^{2}+32x-15x+60\right)\left(x-7\right)$$

Combine -36x^{2} and -8x^{2} to get -44x^{2}.

$$\left(2x^{4}+x^{3}-44x^{2}+32x-15x+60\right)\left(x-7\right)$$

Combine 32x and -15x to get 17x.

$$\left(2x^{4}+x^{3}-44x^{2}+17x+60\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of 2x^{4}+x^{3}-44x^{2}+17x+60 by each term of x-7.

$$2x^{5}-14x^{4}+x^{4}-7x^{3}-44x^{3}+308x^{2}+17x^{2}-119x+60x-420$$

Combine -14x^{4} and x^{4} to get -13x^{4}.

$$2x^{5}-13x^{4}-7x^{3}-44x^{3}+308x^{2}+17x^{2}-119x+60x-420$$

Combine -7x^{3} and -44x^{3} to get -51x^{3}.

$$2x^{5}-13x^{4}-51x^{3}+308x^{2}+17x^{2}-119x+60x-420$$

Combine 308x^{2} and 17x^{2} to get 325x^{2}.

$$2x^{5}-13x^{4}-51x^{3}+325x^{2}-119x+60x-420$$

Combine -119x and 60x to get -59x.

$$2x^{5}-13x^{4}-51x^{3}+325x^{2}-59x-420$$

Expand

$$2x^{5}-13x^{4}-51x^{3}+325x^{2}-59x-420$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-3 by each term of x+5.

$$\left(2x^{2}+10x-3x-15\right)\left(x+1\right)\left(x-4\right)\left(x-7\right)$$

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

$$\left(2x^{2}+7x-15\right)\left(x+1\right)\left(x-4\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of 2x^{2}+7x-15 by each term of x+1.

$$\left(2x^{3}+2x^{2}+7x^{2}+7x-15x-15\right)\left(x-4\right)\left(x-7\right)$$

Combine 2x^{2} and 7x^{2} to get 9x^{2}.

$$\left(2x^{3}+9x^{2}+7x-15x-15\right)\left(x-4\right)\left(x-7\right)$$

Combine 7x and -15x to get -8x.

$$\left(2x^{3}+9x^{2}-8x-15\right)\left(x-4\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of 2x^{3}+9x^{2}-8x-15 by each term of x-4.

$$\left(2x^{4}-8x^{3}+9x^{3}-36x^{2}-8x^{2}+32x-15x+60\right)\left(x-7\right)$$

Combine -8x^{3} and 9x^{3} to get x^{3}.

$$\left(2x^{4}+x^{3}-36x^{2}-8x^{2}+32x-15x+60\right)\left(x-7\right)$$

Combine -36x^{2} and -8x^{2} to get -44x^{2}.

$$\left(2x^{4}+x^{3}-44x^{2}+32x-15x+60\right)\left(x-7\right)$$

Combine 32x and -15x to get 17x.

$$\left(2x^{4}+x^{3}-44x^{2}+17x+60\right)\left(x-7\right)$$

Apply the distributive property by multiplying each term of 2x^{4}+x^{3}-44x^{2}+17x+60 by each term of x-7.

$$2x^{5}-14x^{4}+x^{4}-7x^{3}-44x^{3}+308x^{2}+17x^{2}-119x+60x-420$$

Combine -14x^{4} and x^{4} to get -13x^{4}.

$$2x^{5}-13x^{4}-7x^{3}-44x^{3}+308x^{2}+17x^{2}-119x+60x-420$$

Combine -7x^{3} and -44x^{3} to get -51x^{3}.

$$2x^{5}-13x^{4}-51x^{3}+308x^{2}+17x^{2}-119x+60x-420$$

Combine 308x^{2} and 17x^{2} to get 325x^{2}.

$$2x^{5}-13x^{4}-51x^{3}+325x^{2}-119x+60x-420$$

Combine -119x and 60x to get -59x.

$$2x^{5}-13x^{4}-51x^{3}+325x^{2}-59x-420$$