Solve (x+5)(x+3)(x-3)(x-4)

$$(x+5)(x+3)(x-3)(x-4)$$

Evaluate

$$\left(x-4\right)\left(x+5\right)\left(x^{2}-9\right)$$

Solution Steps

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

$$\left(x^{2}+3x+5x+15\right)\left(x-3\right)\left(x-4\right)$$

Combine 3x and 5x to get 8x.

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

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

$$\left(x^{3}-3x^{2}+8x^{2}-24x+15x-45\right)\left(x-4\right)$$

Combine -3x^{2} and 8x^{2} to get 5x^{2}.

$$\left(x^{3}+5x^{2}-24x+15x-45\right)\left(x-4\right)$$

Combine -24x and 15x to get -9x.

$$\left(x^{3}+5x^{2}-9x-45\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x^{3}+5x^{2}-9x-45 by each term of x-4.

$$x^{4}-4x^{3}+5x^{3}-20x^{2}-9x^{2}+36x-45x+180$$

Combine -4x^{3} and 5x^{3} to get x^{3}.

$$x^{4}+x^{3}-20x^{2}-9x^{2}+36x-45x+180$$

Combine -20x^{2} and -9x^{2} to get -29x^{2}.

$$x^{4}+x^{3}-29x^{2}+36x-45x+180$$

Combine 36x and -45x to get -9x.

$$x^{4}+x^{3}-29x^{2}-9x+180$$

Expand

$$x^{4}+x^{3}-29x^{2}-9x+180$$

Solution Steps

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

$$\left(x^{2}+3x+5x+15\right)\left(x-3\right)\left(x-4\right)$$

Combine 3x and 5x to get 8x.

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

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

$$\left(x^{3}-3x^{2}+8x^{2}-24x+15x-45\right)\left(x-4\right)$$

Combine -3x^{2} and 8x^{2} to get 5x^{2}.

$$\left(x^{3}+5x^{2}-24x+15x-45\right)\left(x-4\right)$$

Combine -24x and 15x to get -9x.

$$\left(x^{3}+5x^{2}-9x-45\right)\left(x-4\right)$$

Apply the distributive property by multiplying each term of x^{3}+5x^{2}-9x-45 by each term of x-4.

$$x^{4}-4x^{3}+5x^{3}-20x^{2}-9x^{2}+36x-45x+180$$

Combine -4x^{3} and 5x^{3} to get x^{3}.

$$x^{4}+x^{3}-20x^{2}-9x^{2}+36x-45x+180$$

Combine -20x^{2} and -9x^{2} to get -29x^{2}.

$$x^{4}+x^{3}-29x^{2}+36x-45x+180$$

Combine 36x and -45x to get -9x.

$$x^{4}+x^{3}-29x^{2}-9x+180$$