Solve (x+2)(x+5)(x-2)(x+9)

$$( x + 2 ) ( x + 5 ) ( x - 2 ) ( x + 9 )$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x+2 by each term of x+5.

$$\left(x^{2}+5x+2x+10\right)\left(x-2\right)\left(x+9\right)$$

Combine 5x and 2x to get 7x.

$$\left(x^{2}+7x+10\right)\left(x-2\right)\left(x+9\right)$$

Apply the distributive property by multiplying each term of x^{2}+7x+10 by each term of x-2.

$$\left(x^{3}-2x^{2}+7x^{2}-14x+10x-20\right)\left(x+9\right)$$

Combine -2x^{2} and 7x^{2} to get 5x^{2}.

$$\left(x^{3}+5x^{2}-14x+10x-20\right)\left(x+9\right)$$

Combine -14x and 10x to get -4x.

$$\left(x^{3}+5x^{2}-4x-20\right)\left(x+9\right)$$

Apply the distributive property by multiplying each term of x^{3}+5x^{2}-4x-20 by each term of x+9.

$$x^{4}+9x^{3}+5x^{3}+45x^{2}-4x^{2}-36x-20x-180$$

Combine 9x^{3} and 5x^{3} to get 14x^{3}.

$$x^{4}+14x^{3}+45x^{2}-4x^{2}-36x-20x-180$$

Combine 45x^{2} and -4x^{2} to get 41x^{2}.

$$x^{4}+14x^{3}+41x^{2}-36x-20x-180$$

Combine -36x and -20x to get -56x.

$$x^{4}+14x^{3}+41x^{2}-56x-180$$

Expand

$$x^{4}+14x^{3}+41x^{2}-56x-180$$

Solution Steps

Apply the distributive property by multiplying each term of x+2 by each term of x+5.

$$\left(x^{2}+5x+2x+10\right)\left(x-2\right)\left(x+9\right)$$

Combine 5x and 2x to get 7x.

$$\left(x^{2}+7x+10\right)\left(x-2\right)\left(x+9\right)$$

Apply the distributive property by multiplying each term of x^{2}+7x+10 by each term of x-2.

$$\left(x^{3}-2x^{2}+7x^{2}-14x+10x-20\right)\left(x+9\right)$$

Combine -2x^{2} and 7x^{2} to get 5x^{2}.

$$\left(x^{3}+5x^{2}-14x+10x-20\right)\left(x+9\right)$$

Combine -14x and 10x to get -4x.

$$\left(x^{3}+5x^{2}-4x-20\right)\left(x+9\right)$$

Apply the distributive property by multiplying each term of x^{3}+5x^{2}-4x-20 by each term of x+9.

$$x^{4}+9x^{3}+5x^{3}+45x^{2}-4x^{2}-36x-20x-180$$

Combine 9x^{3} and 5x^{3} to get 14x^{3}.

$$x^{4}+14x^{3}+45x^{2}-4x^{2}-36x-20x-180$$

Combine 45x^{2} and -4x^{2} to get 41x^{2}.

$$x^{4}+14x^{3}+41x^{2}-36x-20x-180$$

Combine -36x and -20x to get -56x.

$$x^{4}+14x^{3}+41x^{2}-56x-180$$