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

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

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x+4.

$$\left(x^{2}+4x-3x-12\right)\left(x-5\right)\left(x+1\right)$$

Combine 4x and -3x to get x.

$$\left(x^{2}+x-12\right)\left(x-5\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of x^{2}+x-12 by each term of x-5.

$$\left(x^{3}-5x^{2}+x^{2}-5x-12x+60\right)\left(x+1\right)$$

Combine -5x^{2} and x^{2} to get -4x^{2}.

$$\left(x^{3}-4x^{2}-5x-12x+60\right)\left(x+1\right)$$

Combine -5x and -12x to get -17x.

$$\left(x^{3}-4x^{2}-17x+60\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of x^{3}-4x^{2}-17x+60 by each term of x+1.

$$x^{4}+x^{3}-4x^{3}-4x^{2}-17x^{2}-17x+60x+60$$

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

$$x^{4}-3x^{3}-4x^{2}-17x^{2}-17x+60x+60$$

Combine -4x^{2} and -17x^{2} to get -21x^{2}.

$$x^{4}-3x^{3}-21x^{2}-17x+60x+60$$

Combine -17x and 60x to get 43x.

$$x^{4}-3x^{3}-21x^{2}+43x+60$$

Expand

$$x^{4}-3x^{3}-21x^{2}+43x+60$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x+4.

$$\left(x^{2}+4x-3x-12\right)\left(x-5\right)\left(x+1\right)$$

Combine 4x and -3x to get x.

$$\left(x^{2}+x-12\right)\left(x-5\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of x^{2}+x-12 by each term of x-5.

$$\left(x^{3}-5x^{2}+x^{2}-5x-12x+60\right)\left(x+1\right)$$

Combine -5x^{2} and x^{2} to get -4x^{2}.

$$\left(x^{3}-4x^{2}-5x-12x+60\right)\left(x+1\right)$$

Combine -5x and -12x to get -17x.

$$\left(x^{3}-4x^{2}-17x+60\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of x^{3}-4x^{2}-17x+60 by each term of x+1.

$$x^{4}+x^{3}-4x^{3}-4x^{2}-17x^{2}-17x+60x+60$$

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

$$x^{4}-3x^{3}-4x^{2}-17x^{2}-17x+60x+60$$

Combine -4x^{2} and -17x^{2} to get -21x^{2}.

$$x^{4}-3x^{3}-21x^{2}-17x+60x+60$$

Combine -17x and 60x to get 43x.

$$x^{4}-3x^{3}-21x^{2}+43x+60$$