Solve (x-7)(x+9)(x-8)(x+4)

$$( x - 7 ) ( x + 9 ) ( x - 8 ) ( x + 4 )$$

Evaluate

$$\left(x-8\right)\left(x-7\right)\left(x+4\right)\left(x+9\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-7 by each term of x+9.

$$\left(x^{2}+9x-7x-63\right)\left(x-8\right)\left(x+4\right)$$

Combine 9x and -7x to get 2x.

$$\left(x^{2}+2x-63\right)\left(x-8\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{2}+2x-63 by each term of x-8.

$$\left(x^{3}-8x^{2}+2x^{2}-16x-63x+504\right)\left(x+4\right)$$

Combine -8x^{2} and 2x^{2} to get -6x^{2}.

$$\left(x^{3}-6x^{2}-16x-63x+504\right)\left(x+4\right)$$

Combine -16x and -63x to get -79x.

$$\left(x^{3}-6x^{2}-79x+504\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{3}-6x^{2}-79x+504 by each term of x+4.

$$x^{4}+4x^{3}-6x^{3}-24x^{2}-79x^{2}-316x+504x+2016$$

Combine 4x^{3} and -6x^{3} to get -2x^{3}.

$$x^{4}-2x^{3}-24x^{2}-79x^{2}-316x+504x+2016$$

Combine -24x^{2} and -79x^{2} to get -103x^{2}.

$$x^{4}-2x^{3}-103x^{2}-316x+504x+2016$$

Combine -316x and 504x to get 188x.

$$x^{4}-2x^{3}-103x^{2}+188x+2016$$

Expand

$$x^{4}-2x^{3}-103x^{2}+188x+2016$$

Solution Steps

Apply the distributive property by multiplying each term of x-7 by each term of x+9.

$$\left(x^{2}+9x-7x-63\right)\left(x-8\right)\left(x+4\right)$$

Combine 9x and -7x to get 2x.

$$\left(x^{2}+2x-63\right)\left(x-8\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{2}+2x-63 by each term of x-8.

$$\left(x^{3}-8x^{2}+2x^{2}-16x-63x+504\right)\left(x+4\right)$$

Combine -8x^{2} and 2x^{2} to get -6x^{2}.

$$\left(x^{3}-6x^{2}-16x-63x+504\right)\left(x+4\right)$$

Combine -16x and -63x to get -79x.

$$\left(x^{3}-6x^{2}-79x+504\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of x^{3}-6x^{2}-79x+504 by each term of x+4.

$$x^{4}+4x^{3}-6x^{3}-24x^{2}-79x^{2}-316x+504x+2016$$

Combine 4x^{3} and -6x^{3} to get -2x^{3}.

$$x^{4}-2x^{3}-24x^{2}-79x^{2}-316x+504x+2016$$

Combine -24x^{2} and -79x^{2} to get -103x^{2}.

$$x^{4}-2x^{3}-103x^{2}-316x+504x+2016$$

Combine -316x and 504x to get 188x.

$$x^{4}-2x^{3}-103x^{2}+188x+2016$$