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

$$( 3 x + 5 ) ( 3 x - 2 ) - ( 3 x - 2 ) ( 3 x + 5 )$$

Evaluate

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Solution Steps

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

$$9x^{2}-6x+15x-10-\left(3x-2\right)\left(3x+5\right)$$

Combine -6x and 15x to get 9x.

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

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

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

Combine 15x and -6x to get 9x.

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

To find the opposite of 9x^{2}+9x-10, find the opposite of each term.

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

The opposite of -10 is 10.

$$9x^{2}+9x-10-9x^{2}-9x+10$$

Combine 9x^{2} and -9x^{2} to get 0.

$$9x-10-9x+10$$

Combine 9x and -9x to get 0.

$$-10+10$$

Add -10 and 10 to get 0.

$$0$$

Factor

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Solution Steps

Factor out common term 3x-2 by using distributive property.

$$\left(3x-2\right)\left(3x+5-\left(3x+5\right)\right)$$

Consider 3x+5-\left(3x+5\right). Simplify.

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