Solve (x+3)(x+1)(x-3)(x-5)

$$( x + 3 ) ( x + 1 ) ( x - 3 ) ( x - 5 )$$

Evaluate

$$\left(x-5\right)\left(x+1\right)\left(x^{2}-9\right)$$

Solution Steps

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

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

Combine x and 3x to get 4x.

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

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

$$\left(x^{3}-3x^{2}+4x^{2}-12x+3x-9\right)\left(x-5\right)$$

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

$$\left(x^{3}+x^{2}-12x+3x-9\right)\left(x-5\right)$$

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

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

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

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

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

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

Combine -5x^{2} and -9x^{2} to get -14x^{2}.

$$x^{4}-4x^{3}-14x^{2}+45x-9x+45$$

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

$$x^{4}-4x^{3}-14x^{2}+36x+45$$

Expand

$$x^{4}-4x^{3}-14x^{2}+36x+45$$

Solution Steps

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

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

Combine x and 3x to get 4x.

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

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

$$\left(x^{3}-3x^{2}+4x^{2}-12x+3x-9\right)\left(x-5\right)$$

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

$$\left(x^{3}+x^{2}-12x+3x-9\right)\left(x-5\right)$$

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

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

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

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

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

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

Combine -5x^{2} and -9x^{2} to get -14x^{2}.

$$x^{4}-4x^{3}-14x^{2}+45x-9x+45$$

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

$$x^{4}-4x^{3}-14x^{2}+36x+45$$