Solve (x-1)(x-3)(x+3)(x+4)+24=

$$(x-1)(x-3)(x+3)(x+4)+24=$$

Evaluate

$$\left(x-1\right)\left(x+4\right)\left(x^{2}-9\right)+24$$

Solution Steps

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

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

Combine -3x and -x to get -4x.

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

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

$$\left(x^{3}+3x^{2}-4x^{2}-12x+3x+9\right)\left(x+4\right)+24$$

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

$$\left(x^{3}-x^{2}-12x+3x+9\right)\left(x+4\right)+24$$

Combine -12x and 3x to get -9x.

$$\left(x^{3}-x^{2}-9x+9\right)\left(x+4\right)+24$$

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

$$x^{4}+4x^{3}-x^{3}-4x^{2}-9x^{2}-36x+9x+36+24$$

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

$$x^{4}+3x^{3}-4x^{2}-9x^{2}-36x+9x+36+24$$

Combine -4x^{2} and -9x^{2} to get -13x^{2}.

$$x^{4}+3x^{3}-13x^{2}-36x+9x+36+24$$

Combine -36x and 9x to get -27x.

$$x^{4}+3x^{3}-13x^{2}-27x+36+24$$

Add 36 and 24 to get 60.

$$x^{4}+3x^{3}-13x^{2}-27x+60$$

Expand

$$x^{4}+3x^{3}-13x^{2}-27x+60$$

Solution Steps

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

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

Combine -3x and -x to get -4x.

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

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

$$\left(x^{3}+3x^{2}-4x^{2}-12x+3x+9\right)\left(x+4\right)+24$$

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

$$\left(x^{3}-x^{2}-12x+3x+9\right)\left(x+4\right)+24$$

Combine -12x and 3x to get -9x.

$$\left(x^{3}-x^{2}-9x+9\right)\left(x+4\right)+24$$

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

$$x^{4}+4x^{3}-x^{3}-4x^{2}-9x^{2}-36x+9x+36+24$$

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

$$x^{4}+3x^{3}-4x^{2}-9x^{2}-36x+9x+36+24$$

Combine -4x^{2} and -9x^{2} to get -13x^{2}.

$$x^{4}+3x^{3}-13x^{2}-36x+9x+36+24$$

Combine -36x and 9x to get -27x.

$$x^{4}+3x^{3}-13x^{2}-27x+36+24$$

Add 36 and 24 to get 60.

$$x^{4}+3x^{3}-13x^{2}-27x+60$$