Solve a(a-1)-(a^2-b)=4

$$a ( a - 1 ) - ( a ^ { 2 } - b ) = 4$$

Solve for a

$$a=b-4$$

Steps for Solving Linear Equation

Use the distributive property to multiply a by a-1.

$$a^{2}-a-\left(a^{2}-b\right)=4$$

To find the opposite of a^{2}-b, find the opposite of each term.

$$a^{2}-a-a^{2}+b=4$$

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

$$-a+b=4$$

Subtract b from both sides.

$$-a=4-b$$

Divide both sides by -1.

$$\frac{-a}{-1}=\frac{4-b}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$a=\frac{4-b}{-1}$$

Divide 4-b by -1.

$$a=b-4$$

Solve for b

$$b=a+4$$

Solution Steps

Use the distributive property to multiply a by a-1.

$$a^{2}-a-\left(a^{2}-b\right)=4$$

To find the opposite of a^{2}-b, find the opposite of each term.

$$a^{2}-a-a^{2}+b=4$$

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

$$-a+b=4$$

Add a to both sides.

$$b=4+a$$