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 + 9a = 13a

The volume of a cylinder is πr²h:

v = πr²h
v = π(9² x 1)
v = 81π

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.

(2a)(9ab) + (6a²)(2b)
(2 x 9)(a x a x b) + (6 x 2)(a² x b)
(18)(a¹⁺¹ x b) + (12)(a²b)
18a²b + 12a²b
30a²b

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.

2a⁸ + 2a⁸ = 4a⁸

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 = \( \sqrt{a} \) = \( \sqrt{1} \) = 1

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 = 1² + 1²
c² = 2
c = \( \sqrt{2} \)