Solve (2x-5)(3x+7)-(x+3)(x-3)

$$( 2 x - 5 ) ( 3 x + 7 ) - ( x + 3 ) ( x - 3 )$$

Evaluate

$$5x^{2}-x-26$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-5 by each term of 3x+7.

$$6x^{2}+14x-15x-35-\left(x+3\right)\left(x-3\right)$$

Combine 14x and -15x to get -x.

$$6x^{2}-x-35-\left(x+3\right)\left(x-3\right)$$

Consider \left(x+3\right)\left(x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$6x^{2}-x-35-\left(x^{2}-3^{2}\right)$$

Calculate 3 to the power of 2 and get 9.

$$6x^{2}-x-35-\left(x^{2}-9\right)$$

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

$$6x^{2}-x-35-x^{2}-\left(-9\right)$$

The opposite of -9 is 9.

$$6x^{2}-x-35-x^{2}+9$$

Combine 6x^{2} and -x^{2} to get 5x^{2}.

$$5x^{2}-x-35+9$$

Add -35 and 9 to get -26.

$$5x^{2}-x-26$$

Expand

$$5x^{2}-x-26$$

Solution Steps

Apply the distributive property by multiplying each term of 2x-5 by each term of 3x+7.

$$6x^{2}+14x-15x-35-\left(x+3\right)\left(x-3\right)$$

Combine 14x and -15x to get -x.

$$6x^{2}-x-35-\left(x+3\right)\left(x-3\right)$$

Consider \left(x+3\right)\left(x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$6x^{2}-x-35-\left(x^{2}-3^{2}\right)$$

Calculate 3 to the power of 2 and get 9.

$$6x^{2}-x-35-\left(x^{2}-9\right)$$

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

$$6x^{2}-x-35-x^{2}-\left(-9\right)$$

The opposite of -9 is 9.

$$6x^{2}-x-35-x^{2}+9$$

Combine 6x^{2} and -x^{2} to get 5x^{2}.

$$5x^{2}-x-35+9$$

Add -35 and 9 to get -26.

$$5x^{2}-x-26$$