To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -2 as well and sum (Inside, Outside) to equal 1. For this problem, those two numbers are -1 and 2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + y - 2
y² + (-1 + 2)y + (-1 x 2)
(y - 1)(y + 2)

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.

(8a)(5ab) + (4a²)(7b)
(8 x 5)(a x a x b) + (4 x 7)(a² x b)
(40)(a¹⁺¹ x b) + (28)(a²b)
40a²b + 28a²b
68a²b

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, \(c = \sqrt{a + b}\)

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.

5a + 2a = 7a

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 11cm + 9cm + 15cm = 35cm