To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -81 as well and sum (Inside, Outside) to equal 0. For this problem, those two numbers are -9 and 9. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 81
y² + (-9 + 9)y + (-9 x 9)
(y - 9)(y + 9)

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

8a + y = -7
y = -7 - 8a

then substitute the result (-7 - 8a) into the second equation:

6a + 9(-7 - 8a) = 3
6a + (9 x -7) + (9 x -8a) = 3
6a - 63 - 72a = 3
6a - 72a = 3 + 63
-66a = 66
a = \( \frac{66}{-66} \)
a = -1

The volume of a cube is height x length x width:

v = h x l x w
v = 4 x 8 x 1
v = 32

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

4b + 1 > \( \frac{b}{8} \)
8 x (4b + 1) > b
(8 x 4b) + (8 x 1) > b
32b + 8 > b
32b + 8 - b > 0
32b - b > -8
31b > -8
b > \( \frac{-8}{31} \)
b > -\(\frac{8}{31}\)

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).