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

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

Evaluate

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

Solution Steps

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

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

Expand \left(3x\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

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

Calculate 2 to the power of 2 and get 4.

$$9x^{2}-4-\left(2x+1\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of 2x+1 by each term of x-2.

$$9x^{2}-4-\left(2x^{2}-4x+x-2\right)$$

Combine -4x and x to get -3x.

$$9x^{2}-4-\left(2x^{2}-3x-2\right)$$

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

$$9x^{2}-4-2x^{2}-\left(-3x\right)-\left(-2\right)$$

The opposite of -3x is 3x.

$$9x^{2}-4-2x^{2}+3x-\left(-2\right)$$

The opposite of -2 is 2.

$$9x^{2}-4-2x^{2}+3x+2$$

Combine 9x^{2} and -2x^{2} to get 7x^{2}.

$$7x^{2}-4+3x+2$$

Add -4 and 2 to get -2.

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

Expand

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

Solution Steps

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

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

Expand \left(3x\right)^{2}.

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

Calculate 3 to the power of 2 and get 9.

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

Calculate 2 to the power of 2 and get 4.

$$9x^{2}-4-\left(2x+1\right)\left(x-2\right)$$

Apply the distributive property by multiplying each term of 2x+1 by each term of x-2.

$$9x^{2}-4-\left(2x^{2}-4x+x-2\right)$$

Combine -4x and x to get -3x.

$$9x^{2}-4-\left(2x^{2}-3x-2\right)$$

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

$$9x^{2}-4-2x^{2}-\left(-3x\right)-\left(-2\right)$$

The opposite of -3x is 3x.

$$9x^{2}-4-2x^{2}+3x-\left(-2\right)$$

The opposite of -2 is 2.

$$9x^{2}-4-2x^{2}+3x+2$$

Combine 9x^{2} and -2x^{2} to get 7x^{2}.

$$7x^{2}-4+3x+2$$

Add -4 and 2 to get -2.

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