Solve (x-5)(x+6)+(x-3)(x+10)

$$( x - 5 ) ( x + 6 ) + ( x - 3 ) ( x + 10 )$$

Evaluate

$$2\left(x^{2}+4x-30\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x-5 by each term of x+6.

$$x^{2}+6x-5x-30+\left(x-3\right)\left(x+10\right)$$

Combine 6x and -5x to get x.

$$x^{2}+x-30+\left(x-3\right)\left(x+10\right)$$

Apply the distributive property by multiplying each term of x-3 by each term of x+10.

$$x^{2}+x-30+x^{2}+10x-3x-30$$

Combine 10x and -3x to get 7x.

$$x^{2}+x-30+x^{2}+7x-30$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+x-30+7x-30$$

Combine x and 7x to get 8x.

$$2x^{2}+8x-30-30$$

Subtract 30 from -30 to get -60.

$$2x^{2}+8x-60$$

Expand

$$2x^{2}+8x-60$$

Solution Steps

Apply the distributive property by multiplying each term of x-5 by each term of x+6.

$$x^{2}+6x-5x-30+\left(x-3\right)\left(x+10\right)$$

Combine 6x and -5x to get x.

$$x^{2}+x-30+\left(x-3\right)\left(x+10\right)$$

Apply the distributive property by multiplying each term of x-3 by each term of x+10.

$$x^{2}+x-30+x^{2}+10x-3x-30$$

Combine 10x and -3x to get 7x.

$$x^{2}+x-30+x^{2}+7x-30$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$2x^{2}+x-30+7x-30$$

Combine x and 7x to get 8x.

$$2x^{2}+8x-30-30$$

Subtract 30 from -30 to get -60.

$$2x^{2}+8x-60$$