Solve A=(x-1)^2-(x-2)(x-3)+5

$$A = ( x - 1 ) ^ { 2 } - ( x - 2 ) ( x - 3 ) + 5$$

Solve for A

$$A=3x$$

Solution Steps

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

$$A=x^{2}-2x+1-\left(x-2\right)\left(x-3\right)+5$$

Use the distributive property to multiply x-2 by x-3 and combine like terms.

$$A=x^{2}-2x+1-\left(x^{2}-5x+6\right)+5$$

To find the opposite of x^{2}-5x+6, find the opposite of each term.

$$A=x^{2}-2x+1-x^{2}+5x-6+5$$

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

$$A=-2x+1+5x-6+5$$

Combine -2x and 5x to get 3x.

$$A=3x+1-6+5$$

Subtract 6 from 1 to get -5.

$$A=3x-5+5$$

Add -5 and 5 to get 0.

$$A=3x$$

Solve for x

$$x=\frac{A}{3}$$

Steps for Solving Linear Equation

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

$$A=x^{2}-2x+1-\left(x-2\right)\left(x-3\right)+5$$

Use the distributive property to multiply x-2 by x-3 and combine like terms.

$$A=x^{2}-2x+1-\left(x^{2}-5x+6\right)+5$$

To find the opposite of x^{2}-5x+6, find the opposite of each term.

$$A=x^{2}-2x+1-x^{2}+5x-6+5$$

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

$$A=-2x+1+5x-6+5$$

Combine -2x and 5x to get 3x.

$$A=3x+1-6+5$$

Subtract 6 from 1 to get -5.

$$A=3x-5+5$$

Add -5 and 5 to get 0.

$$A=3x$$

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

$$3x=A$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{A}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{A}{3}$$