Solve 2x*(2x-3)-3x*(x-6)-(x+4)^2

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

Evaluate

$$4\left(x-4\right)$$

Solution Steps

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

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$4x^{2}-6x-3x\left(x-6\right)-\left(x^{2}+8x+16\right)$$

To find the opposite of x^{2}+8x+16, find the opposite of each term.

$$4x^{2}-6x-3x\left(x-6\right)-x^{2}-8x-16$$

Use the distributive property to multiply -3x by x-6.

$$4x^{2}-6x-3x^{2}+18x-x^{2}-8x-16$$

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

$$x^{2}-6x+18x-x^{2}-8x-16$$

Combine -6x and 18x to get 12x.

$$x^{2}+12x-x^{2}-8x-16$$

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

$$12x-8x-16$$

Combine 12x and -8x to get 4x.

$$4x-16$$

Expand

$$4x-16$$

Solution Steps

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

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

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+4\right)^{2}.

$$4x^{2}-6x-3x\left(x-6\right)-\left(x^{2}+8x+16\right)$$

To find the opposite of x^{2}+8x+16, find the opposite of each term.

$$4x^{2}-6x-3x\left(x-6\right)-x^{2}-8x-16$$

Use the distributive property to multiply -3x by x-6.

$$4x^{2}-6x-3x^{2}+18x-x^{2}-8x-16$$

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

$$x^{2}-6x+18x-x^{2}-8x-16$$

Combine -6x and 18x to get 12x.

$$x^{2}+12x-x^{2}-8x-16$$

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

$$12x-8x-16$$

Combine 12x and -8x to get 4x.

$$4x-16$$