Solve A=(x+5)^2-(x+4)^2-(x-3)^2+(x-4)^2

$$A = ( x + 5 ) ^ { 2 } - ( x + 4 ) ^ { 2 } - ( x - 3 ) ^ { 2 } + ( x - 4 ) ^ { 2 }$$

Solve for A

$$A=16$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+5\right)^{2}.

$$A=x^{2}+10x+25-\left(x+4\right)^{2}-\left(x-3\right)^{2}+\left(x-4\right)^{2}$$

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

$$A=x^{2}+10x+25-\left(x^{2}+8x+16\right)-\left(x-3\right)^{2}+\left(x-4\right)^{2}$$

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

$$A=x^{2}+10x+25-x^{2}-8x-16-\left(x-3\right)^{2}+\left(x-4\right)^{2}$$

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

$$A=10x+25-8x-16-\left(x-3\right)^{2}+\left(x-4\right)^{2}$$

Combine 10x and -8x to get 2x.

$$A=2x+25-16-\left(x-3\right)^{2}+\left(x-4\right)^{2}$$

Subtract 16 from 25 to get 9.

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

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

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

To find the opposite of x^{2}-6x+9, find the opposite of each term.

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

Combine 2x and 6x to get 8x.

$$A=8x+9-x^{2}-9+\left(x-4\right)^{2}$$

Subtract 9 from 9 to get 0.

$$A=8x-x^{2}+\left(x-4\right)^{2}$$

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

$$A=8x-x^{2}+x^{2}-8x+16$$

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

$$A=8x-8x+16$$

Combine 8x and -8x to get 0.

$$A=16$$

Solve for x (complex solution)

$$x\in \mathrm{C}$$

$$A=16$$

Solve for x

$$x\in \mathrm{R}$$

$$A=16$$