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)(2ab) - (2a²)(8b)
(4 x 2)(a x a x b) - (2 x 8)(a² x b)
(8)(a¹⁺¹ x b) - (16)(a²b)
8a²b - 16a²b
-8a²b

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:

y² + 3y - 27 = 5y - 3
y² + 3y - 27 + 3 = 5y
y² + 3y - 5y - 24 = 0
y² - 2y - 24 = 0

Next, factor the quadratic equation:

y² - 2y - 24 = 0
(y + 4)(y - 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y + 4) or (y - 6) must equal zero:

If (y + 4) = 0, y must equal -4
If (y - 6) = 0, y must equal 6

So the solution is that y = -4 or 6

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(2 + 5)(3)
a = ½(7)(3)
a = ½(21) = \( \frac{21}{2} \)
a = 10\(\frac{1}{2}\)

A rectangle is a parallelogram containing four right angles. Opposite sides (a = c, b = d) are equal and the perimeter is the sum of the lengths of all sides (a + b + c + d) or, comonly, 2 x length x width. The area of a rectangle is length x width. A square is a rectangle with four equal length sides. The perimeter of a square is 4 x length of one side (4s) and the area is the length of one side squared (s²).

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 4. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 10) and (2, -2) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = -3x + 4