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.

(7a)(6ab) + (7a²)(8b)
(7 x 6)(a x a x b) + (7 x 8)(a² x b)
(42)(a¹⁺¹ x b) + (56)(a²b)
42a²b + 56a²b
98a²b

A right angle measures 90 degrees and is the intersection of two perpendicular lines. In diagrams, a right angle is indicated by a small box completing a square with the perpendicular lines.

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 12 as well and sum (Inside, Outside) to equal -7. For this problem, those two numbers are -4 and -3. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 7y + 12
y² + (-4 - 3)y + (-4 x -3)
(y - 4)(y - 3)

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 equal sign and the answer on the other.

-7z - 2 = \( \frac{z}{8} \)
8 x (-7z - 2) = z
(8 x -7z) + (8 x -2) = z
-56z - 16 = z
-56z - 16 - z = 0
-56z - z = 16
-57z = 16
z = \( \frac{16}{-57} \)
z = -\(\frac{16}{57}\)

To solve this equation, isolate the variable for which you are solving (a) on one side of the equation and put everything else on the other side.

-7a - 9x = 2a + 8x + 7
-7a = 2a + 8x + 7 + 9x
-7a - 2a = 8x + 7 + 9x
-9a = 17x + 7
a = \( \frac{17x + 7}{-9} \)
a = \( \frac{17x}{-9} \) + \( \frac{7}{-9} \)
a = -1\(\frac{8}{9}\)x - \(\frac{7}{9}\)