Solve Z=(x-4)^2-(x-2)(x-8)

$$Z = ( x - 4 ) ^ { 2 } - ( x - 2 ) ( x - 8 )$$

Solve for Z

$$Z=2x$$

Solution Steps

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

$$Z=x^{2}-8x+16-\left(x-2\right)\left(x-8\right)$$

Use the distributive property to multiply x-2 by x-8 and combine like terms.

$$Z=x^{2}-8x+16-\left(x^{2}-10x+16\right)$$

To find the opposite of x^{2}-10x+16, find the opposite of each term.

$$Z=x^{2}-8x+16-x^{2}+10x-16$$

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

$$Z=-8x+16+10x-16$$

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

$$Z=2x+16-16$$

Subtract 16 from 16 to get 0.

$$Z=2x$$

Solve for x

$$x=\frac{Z}{2}$$

Steps for Solving Linear Equation

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

$$Z=x^{2}-8x+16-\left(x-2\right)\left(x-8\right)$$

Use the distributive property to multiply x-2 by x-8 and combine like terms.

$$Z=x^{2}-8x+16-\left(x^{2}-10x+16\right)$$

To find the opposite of x^{2}-10x+16, find the opposite of each term.

$$Z=x^{2}-8x+16-x^{2}+10x-16$$

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

$$Z=-8x+16+10x-16$$

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

$$Z=2x+16-16$$

Subtract 16 from 16 to get 0.

$$Z=2x$$

Swap sides so that all variable terms are on the left hand side.

$$2x=Z$$

Divide both sides by 2.

$$\frac{2x}{2}=\frac{Z}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x=\frac{Z}{2}$$