Solve (3x+5)(2x-5)-(9x-5)*(x-5)

$$( 3 x + 5 ) ( 2 x - 5 ) - ( 9 x - 5 ) \cdot ( x - 5 )$$

Evaluate

$$-3x^{2}+45x-50$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+5 by each term of 2x-5.

$$6x^{2}-15x+10x-25-\left(9x-5\right)\left(x-5\right)$$

Combine -15x and 10x to get -5x.

$$6x^{2}-5x-25-\left(9x-5\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of 9x-5 by each term of x-5.

$$6x^{2}-5x-25-\left(9x^{2}-45x-5x+25\right)$$

Combine -45x and -5x to get -50x.

$$6x^{2}-5x-25-\left(9x^{2}-50x+25\right)$$

To find the opposite of 9x^{2}-50x+25, find the opposite of each term.

$$6x^{2}-5x-25-9x^{2}-\left(-50x\right)-25$$

The opposite of -50x is 50x.

$$6x^{2}-5x-25-9x^{2}+50x-25$$

Combine 6x^{2} and -9x^{2} to get -3x^{2}.

$$-3x^{2}-5x-25+50x-25$$

Combine -5x and 50x to get 45x.

$$-3x^{2}+45x-25-25$$

Subtract 25 from -25 to get -50.

$$-3x^{2}+45x-50$$

Expand

$$-3x^{2}+45x-50$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+5 by each term of 2x-5.

$$6x^{2}-15x+10x-25-\left(9x-5\right)\left(x-5\right)$$

Combine -15x and 10x to get -5x.

$$6x^{2}-5x-25-\left(9x-5\right)\left(x-5\right)$$

Apply the distributive property by multiplying each term of 9x-5 by each term of x-5.

$$6x^{2}-5x-25-\left(9x^{2}-45x-5x+25\right)$$

Combine -45x and -5x to get -50x.

$$6x^{2}-5x-25-\left(9x^{2}-50x+25\right)$$

To find the opposite of 9x^{2}-50x+25, find the opposite of each term.

$$6x^{2}-5x-25-9x^{2}-\left(-50x\right)-25$$

The opposite of -50x is 50x.

$$6x^{2}-5x-25-9x^{2}+50x-25$$

Combine 6x^{2} and -9x^{2} to get -3x^{2}.

$$-3x^{2}-5x-25+50x-25$$

Combine -5x and 50x to get 45x.

$$-3x^{2}+45x-25-25$$

Subtract 25 from -25 to get -50.

$$-3x^{2}+45x-50$$