Solve (3x+2)(x-3)-(x-1)*(3x+1)

$$( 3 x + 2 ) ( x - 3 ) - ( x - 1 ) \cdot ( 3 x + 1 )$$

Evaluate

$$-5x-5$$

Solution Steps

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

$$3x^{2}-9x+2x-6-\left(x-1\right)\left(3x+1\right)$$

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

$$3x^{2}-7x-6-\left(x-1\right)\left(3x+1\right)$$

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

$$3x^{2}-7x-6-\left(3x^{2}+x-3x-1\right)$$

Combine x and -3x to get -2x.

$$3x^{2}-7x-6-\left(3x^{2}-2x-1\right)$$

To find the opposite of 3x^{2}-2x-1, find the opposite of each term.

$$3x^{2}-7x-6-3x^{2}-\left(-2x\right)-\left(-1\right)$$

The opposite of -2x is 2x.

$$3x^{2}-7x-6-3x^{2}+2x-\left(-1\right)$$

The opposite of -1 is 1.

$$3x^{2}-7x-6-3x^{2}+2x+1$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-7x-6+2x+1$$

Combine -7x and 2x to get -5x.

$$-5x-6+1$$

Add -6 and 1 to get -5.

$$-5x-5$$

Expand

$$-5x-5$$

Solution Steps

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

$$3x^{2}-9x+2x-6-\left(x-1\right)\left(3x+1\right)$$

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

$$3x^{2}-7x-6-\left(x-1\right)\left(3x+1\right)$$

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

$$3x^{2}-7x-6-\left(3x^{2}+x-3x-1\right)$$

Combine x and -3x to get -2x.

$$3x^{2}-7x-6-\left(3x^{2}-2x-1\right)$$

To find the opposite of 3x^{2}-2x-1, find the opposite of each term.

$$3x^{2}-7x-6-3x^{2}-\left(-2x\right)-\left(-1\right)$$

The opposite of -2x is 2x.

$$3x^{2}-7x-6-3x^{2}+2x-\left(-1\right)$$

The opposite of -1 is 1.

$$3x^{2}-7x-6-3x^{2}+2x+1$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-7x-6+2x+1$$

Combine -7x and 2x to get -5x.

$$-5x-6+1$$

Add -6 and 1 to get -5.

$$-5x-5$$