Solve (2)9(x+2)(x-2)-(3x-2)^2

$$( 2 ) 9 ( x + 2 ) ( x - 2 ) - ( 3 x - 2 ) ^ { 2 }$$

Evaluate

$$9x^{2}+12x-76$$

Solution Steps

Multiply 2 and 9 to get 18.

$$18\left(x+2\right)\left(x-2\right)-\left(3x-2\right)^{2}$$

Use the distributive property to multiply 18 by x+2.

$$\left(18x+36\right)\left(x-2\right)-\left(3x-2\right)^{2}$$

Use the distributive property to multiply 18x+36 by x-2 and combine like terms.

$$18x^{2}-72-\left(3x-2\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2\right)^{2}.

$$18x^{2}-72-\left(9x^{2}-12x+4\right)$$

To find the opposite of 9x^{2}-12x+4, find the opposite of each term.

$$18x^{2}-72-9x^{2}+12x-4$$

Combine 18x^{2} and -9x^{2} to get 9x^{2}.

$$9x^{2}-72+12x-4$$

Subtract 4 from -72 to get -76.

$$9x^{2}-76+12x$$

Expand

$$9x^{2}+12x-76$$

Solution Steps

Multiply 2 and 9 to get 18.

$$18\left(x+2\right)\left(x-2\right)-\left(3x-2\right)^{2}$$

Use the distributive property to multiply 18 by x+2.

$$\left(18x+36\right)\left(x-2\right)-\left(3x-2\right)^{2}$$

Use the distributive property to multiply 18x+36 by x-2 and combine like terms.

$$18x^{2}-72-\left(3x-2\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-2\right)^{2}.

$$18x^{2}-72-\left(9x^{2}-12x+4\right)$$

To find the opposite of 9x^{2}-12x+4, find the opposite of each term.

$$18x^{2}-72-9x^{2}+12x-4$$

Combine 18x^{2} and -9x^{2} to get 9x^{2}.

$$9x^{2}-72+12x-4$$

Subtract 4 from -72 to get -76.

$$9x^{2}-76+12x$$