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.

4a - 8a = -4a

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(5a)(9ab) + (9a²)(8b)
(5 x 9)(a x a x b) + (9 x 8)(a² x b)
(45)(a¹⁺¹ x b) + (72)(a²b)
45a²b + 72a²b
117a²b

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:

x² + 7x + 23 = -4x + 5
x² + 7x + 23 - 5 = -4x
x² + 7x + 4x + 18 = 0
x² + 11x + 18 = 0

Next, factor the quadratic equation:

x² + 11x + 18 = 0
(x + 2)(x + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (x + 2) or (x + 9) must equal zero:

If (x + 2) = 0, x must equal -2
If (x + 9) = 0, x must equal -9

So the solution is that x = -2 or -9

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).

To solve this equation, 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.)

-7c(c - y)
-7(5)(5 + 8)
-7(5)(13)
(-35)(13)
-455