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

p = x + y + z
p = 9cm + 5cm + 9cm = 23cm

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 42 as well and sum (Inside, Outside) to equal 13. For this problem, those two numbers are 6 and 7. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 13y + 42
y² + (6 + 7)y + (6 x 7)
(y + 6)(y + 7)

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.

3a⁸ + 6a⁸ = 9a⁸

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(2²) + 2π(2 x 1)
sa = 2π(4) + 2π(2)
sa = (2 x 4)π + (2 x 2)π
sa = 8π + 4π
sa = 12π