To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

7a - 5a = 2a

To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y - 3)(y - 7)
(y x y) + (y x -7) + (-3 x y) + (-3 x -7)
y² - 7y - 3y + 21
y² - 10y + 21

When solving an equation with two variables, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

c² - 4c + 17 = 5c - 1
c² - 4c + 17 + 1 = 5c
c² - 4c - 5c + 18 = 0
c² - 9c + 18 = 0

Next, factor the quadratic equation:

c² - 9c + 18 = 0
(c - 3)(c - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c - 3) or (c - 6) must equal zero:

If (c - 3) = 0, c must equal 3
If (c - 6) = 0, c must equal 6

So the solution is that c = 3 or 6