Solve 3(x+2)*(x-2)-4(x+2)*(x+2)+2x*(x-2)

$$3 ( x + 2 ) \cdot ( x - 2 ) - 4 ( x + 2 ) \cdot ( x + 2 ) + 2 x \cdot ( x - 2 )$$

Evaluate

$$\left(x-10\right)^{2}-128$$

Solution Steps

Multiply x+2 and x+2 to get \left(x+2\right)^{2}.

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

Use the distributive property to multiply 3 by x+2.

$$\left(3x+6\right)\left(x-2\right)-4\left(x+2\right)^{2}+2x\left(x-2\right)$$

Apply the distributive property by multiplying each term of 3x+6 by each term of x-2.

$$3x^{2}-6x+6x-12-4\left(x+2\right)^{2}+2x\left(x-2\right)$$

Combine -6x and 6x to get 0.

$$3x^{2}-12-4\left(x+2\right)^{2}+2x\left(x-2\right)$$

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

$$3x^{2}-12-4\left(x^{2}+4x+4\right)+2x\left(x-2\right)$$

Use the distributive property to multiply -4 by x^{2}+4x+4.

$$3x^{2}-12-4x^{2}-16x-16+2x\left(x-2\right)$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$-x^{2}-12-16x-16+2x\left(x-2\right)$$

Subtract 16 from -12 to get -28.

$$-x^{2}-28-16x+2x\left(x-2\right)$$

Use the distributive property to multiply 2x by x-2.

$$-x^{2}-28-16x+2x^{2}-4x$$

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

$$x^{2}-28-16x-4x$$

Combine -16x and -4x to get -20x.

$$x^{2}-28-20x$$

Expand

$$x^{2}-20x-28$$

Solution Steps

Multiply x+2 and x+2 to get \left(x+2\right)^{2}.

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

Use the distributive property to multiply 3 by x+2.

$$\left(3x+6\right)\left(x-2\right)-4\left(x+2\right)^{2}+2x\left(x-2\right)$$

Apply the distributive property by multiplying each term of 3x+6 by each term of x-2.

$$3x^{2}-6x+6x-12-4\left(x+2\right)^{2}+2x\left(x-2\right)$$

Combine -6x and 6x to get 0.

$$3x^{2}-12-4\left(x+2\right)^{2}+2x\left(x-2\right)$$

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

$$3x^{2}-12-4\left(x^{2}+4x+4\right)+2x\left(x-2\right)$$

Use the distributive property to multiply -4 by x^{2}+4x+4.

$$3x^{2}-12-4x^{2}-16x-16+2x\left(x-2\right)$$

Combine 3x^{2} and -4x^{2} to get -x^{2}.

$$-x^{2}-12-16x-16+2x\left(x-2\right)$$

Subtract 16 from -12 to get -28.

$$-x^{2}-28-16x+2x\left(x-2\right)$$

Use the distributive property to multiply 2x by x-2.

$$-x^{2}-28-16x+2x^{2}-4x$$

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

$$x^{2}-28-16x-4x$$

Combine -16x and -4x to get -20x.

$$x^{2}-28-20x$$