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.

(4a)(6ab) - (4a²)(3b)
(4 x 6)(a x a x b) - (4 x 3)(a² x b)
(24)(a¹⁺¹ x b) - (12)(a²b)
24a²b - 12a²b
12a²b

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

c² = a² + b²
c² = 3² + 6²
c² = 9 + 36
c² = 45
c = \( \sqrt{45} \)

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\( \sqrt{2} \)

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

sa = 2πr² + 2πrh
sa = 2π(2²) + 2π(2 x 3)
sa = 2π(4) + 2π(6)
sa = (2 x 4)π + (2 x 6)π
sa = 8π + 12π
sa = 20π

The formula for area is πr². Radius is circle \( \frac{diameter}{2} \):

r = \( \frac{d}{2} \)
r = \( \frac{8}{2} \)
r = 4
a = πr²
a = π(4²)
a = 16π