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

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

Evaluate

$$10x+9$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$4x^{2}+4x+1-2\left(x+2\right)\left(x-2\right)-\left(-2x\left(3-x\right)\right)$$

The opposite of -2x\left(3-x\right) is 2x\left(3-x\right).

$$4x^{2}+4x+1-2\left(x+2\right)\left(x-2\right)+2x\left(3-x\right)$$

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

$$4x^{2}+4x+1-2\left(x+2\right)\left(x-2\right)+6x-2x^{2}$$

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

$$4x^{2}+4x+1+\left(-2x-4\right)\left(x-2\right)+6x-2x^{2}$$

Use the distributive property to multiply -2x-4 by x-2 and combine like terms.

$$4x^{2}+4x+1-2x^{2}+8+6x-2x^{2}$$

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

$$2x^{2}+4x+1+8+6x-2x^{2}$$

Add 1 and 8 to get 9.

$$2x^{2}+4x+9+6x-2x^{2}$$

Combine 4x and 6x to get 10x.

$$2x^{2}+10x+9-2x^{2}$$

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

$$10x+9$$

Expand

$$10x+9$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+1\right)^{2}.

$$4x^{2}+4x+1-2\left(x+2\right)\left(x-2\right)-\left(-2x\left(3-x\right)\right)$$

The opposite of -2x\left(3-x\right) is 2x\left(3-x\right).

$$4x^{2}+4x+1-2\left(x+2\right)\left(x-2\right)+2x\left(3-x\right)$$

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

$$4x^{2}+4x+1-2\left(x+2\right)\left(x-2\right)+6x-2x^{2}$$

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

$$4x^{2}+4x+1+\left(-2x-4\right)\left(x-2\right)+6x-2x^{2}$$

Use the distributive property to multiply -2x-4 by x-2 and combine like terms.

$$4x^{2}+4x+1-2x^{2}+8+6x-2x^{2}$$

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

$$2x^{2}+4x+1+8+6x-2x^{2}$$

Add 1 and 8 to get 9.

$$2x^{2}+4x+9+6x-2x^{2}$$

Combine 4x and 6x to get 10x.

$$2x^{2}+10x+9-2x^{2}$$

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

$$10x+9$$