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

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

Evaluate

$$x\left(21-x\right)$$

Solution Steps

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

$$4x^{2}+12x+9-\left(2x-3\right)^{2}-x\left(x+3\right)$$

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

$$4x^{2}+12x+9-\left(4x^{2}-12x+9\right)-x\left(x+3\right)$$

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

$$4x^{2}+12x+9-4x^{2}+12x-9-x\left(x+3\right)$$

Combine 4x^{2} and -4x^{2} to get 0.

$$12x+9+12x-9-x\left(x+3\right)$$

Combine 12x and 12x to get 24x.

$$24x+9-9-x\left(x+3\right)$$

Subtract 9 from 9 to get 0.

$$24x-x\left(x+3\right)$$

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

$$24x-\left(x^{2}+3x\right)$$

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

$$24x-x^{2}-3x$$

Combine 24x and -3x to get 21x.

$$21x-x^{2}$$

Expand

$$21x-x^{2}$$

Solution Steps

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

$$4x^{2}+12x+9-\left(2x-3\right)^{2}-x\left(x+3\right)$$

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

$$4x^{2}+12x+9-\left(4x^{2}-12x+9\right)-x\left(x+3\right)$$

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

$$4x^{2}+12x+9-4x^{2}+12x-9-x\left(x+3\right)$$

Combine 4x^{2} and -4x^{2} to get 0.

$$12x+9+12x-9-x\left(x+3\right)$$

Combine 12x and 12x to get 24x.

$$24x+9-9-x\left(x+3\right)$$

Subtract 9 from 9 to get 0.

$$24x-x\left(x+3\right)$$

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

$$24x-\left(x^{2}+3x\right)$$

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

$$24x-x^{2}-3x$$

Combine 24x and -3x to get 21x.

$$21x-x^{2}$$