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 first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

a² + 6a - 27 = 0
(a - 3)(a + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (a - 3) or (a + 9) must equal zero:

If (a - 3) = 0, a must equal 3
If (a + 9) = 0, a must equal -9

So the solution is that a = 3 or -9

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:

b² + 5b - 53 = 4b + 3
b² + 5b - 53 - 3 = 4b
b² + 5b - 4b - 56 = 0
b² + b - 56 = 0

Next, factor the quadratic equation:

b² + b - 56 = 0
(b - 7)(b + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 7) or (b + 8) must equal zero:

If (b - 7) = 0, b must equal 7
If (b + 8) = 0, b must equal -8

So the solution is that b = 7 or -8

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)(7b)
(7 x 6)(a x a x b) + (7 x 7)(a² x b)
(42)(a¹⁺¹ x b) + (49)(a²b)
42a²b + 49a²b
91a²b

A circle is a figure in which each point around its perimeter is an equal distance from the center. The radius of a circle is the distance between the center and any point along its perimeter. A chord is a line segment that connects any two points along its perimeter. The diameter of a circle is the length of a chord that passes through the center of the circle and equals twice the circle's radius (2r).