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 1 as well and sum (Inside, Outside) to equal 2. For this problem, those two numbers are 1 and 1. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 2y + 1
y² + (1 + 1)y + (1 x 1)
(y + 1)(y + 1)

Perimeter is equal to the sum of the four sides:

p = a + b + c + d
p = 2 + 4 + 8 + 6
p = 20

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)

The formula for area is πr². Radius is circle \( \frac{diameter}{2} \):

r = \( \frac{d}{2} \)
r = \( \frac{8}{2} \)
r = 4
a = πr²
a = π(4²)
a = 16π

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.

(8a)(7ab) - (4a²)(7b)
(8 x 7)(a x a x b) - (4 x 7)(a² x b)
(56)(a¹⁺¹ x b) - (28)(a²b)
56a²b - 28a²b
28a²b