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

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

Evaluate

$$7+2x-7x^{2}$$

Solution Steps

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

$$\left(-x\right)^{2}+6\left(-x\right)+9-2\left(2x-1\right)^{2}$$

Calculate -x to the power of 2 and get x^{2}.

$$x^{2}+6\left(-x\right)+9-2\left(2x-1\right)^{2}$$

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

$$x^{2}+6\left(-x\right)+9-2\left(4x^{2}-4x+1\right)$$

Use the distributive property to multiply -2 by 4x^{2}-4x+1.

$$x^{2}+6\left(-x\right)+9-8x^{2}+8x-2$$

Combine x^{2} and -8x^{2} to get -7x^{2}.

$$-7x^{2}+6\left(-x\right)+9+8x-2$$

Subtract 2 from 9 to get 7.

$$-7x^{2}+6\left(-x\right)+7+8x$$

Multiply 6 and -1 to get -6.

$$-7x^{2}-6x+7+8x$$

Combine -6x and 8x to get 2x.

$$-7x^{2}+2x+7$$

Expand

$$7+2x-7x^{2}$$

Solution Steps

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

$$\left(-x\right)^{2}+6\left(-x\right)+9-2\left(2x-1\right)^{2}$$

Calculate -x to the power of 2 and get x^{2}.

$$x^{2}+6\left(-x\right)+9-2\left(2x-1\right)^{2}$$

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

$$x^{2}+6\left(-x\right)+9-2\left(4x^{2}-4x+1\right)$$

Use the distributive property to multiply -2 by 4x^{2}-4x+1.

$$x^{2}+6\left(-x\right)+9-8x^{2}+8x-2$$

Combine x^{2} and -8x^{2} to get -7x^{2}.

$$-7x^{2}+6\left(-x\right)+9+8x-2$$

Subtract 2 from 9 to get 7.

$$-7x^{2}+6\left(-x\right)+7+8x$$

Multiply 6 and -1 to get -6.

$$-7x^{2}-6x+7+8x$$

Combine -6x and 8x to get 2x.

$$-7x^{2}+2x+7$$