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 8 as well and sum (Inside, Outside) to equal -9. For this problem, those two numbers are -8 and -1. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 9y + 8
y² + (-8 - 1)y + (-8 x -1)
(y - 8)(y - 1)

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

sa = 2πr² + 2πrh
sa = 2π(1²) + 2π(1 x 4)
sa = 2π(1) + 2π(4)
sa = (2 x 1)π + (2 x 4)π
sa = 2π + 8π
sa = 10π

An acute angle measures less than 90°, a right angle measures 90°, and an obtuse angle measures more than 90°.

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.

6a⁹ - 4a⁹ = 2a⁹

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{4} \) = 2

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 2² + 2²
c² = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)