Solve (x+3)^2-(6+x)(x-6)-(1-x)^2+x(x-8)

$$( x + 3 ) ^ { 2 } - ( 6 + x ) ( x - 6 ) - ( 1 - x ) ^ { 2 } + x ( x - 8 )$$

Evaluate

$$44$$

Solution Steps

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

$$x^{2}+6x+9-\left(6+x\right)\left(x-6\right)-\left(1-x\right)^{2}+x\left(x-8\right)$$

Use the distributive property to multiply 6+x by x-6 and combine like terms.

$$x^{2}+6x+9-\left(-36+x^{2}\right)-\left(1-x\right)^{2}+x\left(x-8\right)$$

To find the opposite of -36+x^{2}, find the opposite of each term.

$$x^{2}+6x+9+36-x^{2}-\left(1-x\right)^{2}+x\left(x-8\right)$$

Add 9 and 36 to get 45.

$$x^{2}+6x+45-x^{2}-\left(1-x\right)^{2}+x\left(x-8\right)$$

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

$$6x+45-\left(1-x\right)^{2}+x\left(x-8\right)$$

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

$$6x+45-\left(1-2x+x^{2}\right)+x\left(x-8\right)$$

To find the opposite of 1-2x+x^{2}, find the opposite of each term.

$$6x+45-1+2x-x^{2}+x\left(x-8\right)$$

Subtract 1 from 45 to get 44.

$$6x+44+2x-x^{2}+x\left(x-8\right)$$

Combine 6x and 2x to get 8x.

$$8x+44-x^{2}+x\left(x-8\right)$$

Use the distributive property to multiply x by x-8.

$$8x+44-x^{2}+x^{2}-8x$$

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

$$8x+44-8x$$

Combine 8x and -8x to get 0.

$$44$$

Factor

$$2^{2}\times 11$$