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.

9a + 2a = 11a

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 -5 as well and sum (Inside, Outside) to equal -4. For this problem, those two numbers are -5 and 1. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 4y - 5
y² + (-5 + 1)y + (-5 x 1)
(y - 5)(y + 1)

According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 1² + 5²
c² = 1 + 25
c² = 26
c = \( \sqrt{26} \)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 24° - 30° = 126°

So, d° = 30° + 126° = 156°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 24° = 156°

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.

(7a)(5ab) + (4a²)(2b)
(7 x 5)(a x a x b) + (4 x 2)(a² x b)
(35)(a¹⁺¹ x b) + (8)(a²b)
35a²b + 8a²b
43a²b