Solve (x-7)(x-5)+(3x-10)(x+1)

$$( x - 7 ) ( x - 5 ) + ( 3 x - 10 ) ( x + 1 )$$

Evaluate

$$4x^{2}-19x+25$$

Solution Steps

Apply the distributive property by multiplying each term of x-7 by each term of x-5.

$$x^{2}-5x-7x+35+\left(3x-10\right)\left(x+1\right)$$

Combine -5x and -7x to get -12x.

$$x^{2}-12x+35+\left(3x-10\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 3x-10 by each term of x+1.

$$x^{2}-12x+35+3x^{2}+3x-10x-10$$

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

$$x^{2}-12x+35+3x^{2}-7x-10$$

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

$$4x^{2}-12x+35-7x-10$$

Combine -12x and -7x to get -19x.

$$4x^{2}-19x+35-10$$

Subtract 10 from 35 to get 25.

$$4x^{2}-19x+25$$

Expand

$$4x^{2}-19x+25$$

Solution Steps

Apply the distributive property by multiplying each term of x-7 by each term of x-5.

$$x^{2}-5x-7x+35+\left(3x-10\right)\left(x+1\right)$$

Combine -5x and -7x to get -12x.

$$x^{2}-12x+35+\left(3x-10\right)\left(x+1\right)$$

Apply the distributive property by multiplying each term of 3x-10 by each term of x+1.

$$x^{2}-12x+35+3x^{2}+3x-10x-10$$

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

$$x^{2}-12x+35+3x^{2}-7x-10$$

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

$$4x^{2}-12x+35-7x-10$$

Combine -12x and -7x to get -19x.

$$4x^{2}-19x+35-10$$

Subtract 10 from 35 to get 25.

$$4x^{2}-19x+25$$