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) - (7a²)(6b)
(2 x 9)(a x a x b) - (7 x 6)(a² x b)
(18)(a¹⁺¹ x b) - (42)(a²b)
18a²b - 42a²b
-24a²b

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

c² = a² + b²
c² = 9² + 6²
c² = 81 + 36
c² = 117
c = \( \sqrt{117} \)

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

a² + 12a + 20 = 2a + 4
a² + 12a + 20 - 4 = 2a
a² + 12a - 2a + 16 = 0
a² + 10a + 16 = 0

Next, factor the quadratic equation:

a² + 10a + 16 = 0
(a + 2)(a + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a + 2) or (a + 8) must equal zero:

If (a + 2) = 0, a must equal -2
If (a + 8) = 0, a must equal -8

So the solution is that a = -2 or -8

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.