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)(6ab) - (6a²)(9b)
(2 x 6)(a x a x b) - (6 x 9)(a² x b)
(12)(a¹⁺¹ x b) - (54)(a²b)
12a²b - 54a²b
-42a²b

You need to find the value of b so solve the first equation in terms of y:

-5b + y = -1
y = -1 + 5b

then substitute the result (-1 - -5b) into the second equation:

3b + 5(-1 + 5b) = -6
3b + (5 x -1) + (5 x 5b) = -6
3b - 5 + 25b = -6
3b + 25b = -6 + 5
28b = -1
b = \( \frac{-1}{28} \)
b = -\(\frac{1}{28}\)

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).

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.

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:

c² - 2c - 28 = -c + 2
c² - 2c - 28 - 2 = -c
c² - 2c + c - 30 = 0
c² - c - 30 = 0

Next, factor the quadratic equation:

c² - c - 30 = 0
(c + 5)(c - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (c + 5) or (c - 6) must equal zero:

If (c + 5) = 0, c must equal -5
If (c - 6) = 0, c must equal 6

So the solution is that c = -5 or 6