Solve left(x+1right)left(x+3right)left(x-4right)left(x-6right)-8

$$\left( x+1 \right) \left( x+3 \right) \left( x-4 \right) \left( x-6 \right) -8$$

Evaluate

$$\left(x-6\right)\left(x-4\right)\left(x+1\right)\left(x+3\right)-8$$

Solution Steps

Apply the distributive property by multiplying each term of x+1 by each term of x+3.

$$\left(x^{2}+3x+x+3\right)\left(x-4\right)\left(x-6\right)-8$$

Combine 3x and x to get 4x.

$$\left(x^{2}+4x+3\right)\left(x-4\right)\left(x-6\right)-8$$

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

$$\left(x^{3}-4x^{2}+4x^{2}-16x+3x-12\right)\left(x-6\right)-8$$

Combine -4x^{2} and 4x^{2} to get 0.

$$\left(x^{3}-16x+3x-12\right)\left(x-6\right)-8$$

Combine -16x and 3x to get -13x.

$$\left(x^{3}-13x-12\right)\left(x-6\right)-8$$

Apply the distributive property by multiplying each term of x^{3}-13x-12 by each term of x-6.

$$x^{4}-6x^{3}-13x^{2}+78x-12x+72-8$$

Combine 78x and -12x to get 66x.

$$x^{4}-6x^{3}-13x^{2}+66x+72-8$$

Subtract 8 from 72 to get 64.

$$x^{4}-6x^{3}-13x^{2}+66x+64$$

Expand

$$x^{4}-6x^{3}-13x^{2}+66x+64$$

Solution Steps

Apply the distributive property by multiplying each term of x+1 by each term of x+3.

$$\left(x^{2}+3x+x+3\right)\left(x-4\right)\left(x-6\right)-8$$

Combine 3x and x to get 4x.

$$\left(x^{2}+4x+3\right)\left(x-4\right)\left(x-6\right)-8$$

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

$$\left(x^{3}-4x^{2}+4x^{2}-16x+3x-12\right)\left(x-6\right)-8$$

Combine -4x^{2} and 4x^{2} to get 0.

$$\left(x^{3}-16x+3x-12\right)\left(x-6\right)-8$$

Combine -16x and 3x to get -13x.

$$\left(x^{3}-13x-12\right)\left(x-6\right)-8$$

Apply the distributive property by multiplying each term of x^{3}-13x-12 by each term of x-6.

$$x^{4}-6x^{3}-13x^{2}+78x-12x+72-8$$

Combine 78x and -12x to get 66x.

$$x^{4}-6x^{3}-13x^{2}+66x+72-8$$

Subtract 8 from 72 to get 64.

$$x^{4}-6x^{3}-13x^{2}+66x+64$$