To multiply binomials, use the FOIL method. FOIL stands for First, Outside, Inside, Last and refers to the position of each term in the parentheses:

(y + 1)(y - 8)
(y x y) + (y x -8) + (1 x y) + (1 x -8)
y² - 8y + y - 8
y² - 7y - 8

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 = \( \sqrt{a} \) = \( \sqrt{9} \) = 3

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 = 3² + 3²
c² = 18
c = \( \sqrt{18} \) = \( \sqrt{9 x 2} \) = \( \sqrt{9} \) \( \sqrt{2} \)
c = 3\( \sqrt{2} \)

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

r = \( \frac{d}{2} \)
r = \( \frac{4}{2} \)
r = 2
a = πr²
a = π(2²)
a = 4π

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.

8a + 4x = -9a + x - 7
8a = -9a + x - 7 - 4x
8a + 9a = x - 7 - 4x
17a = -3x - 7
a = \( \frac{-3x - 7}{17} \)
a = \( \frac{-3x}{17} \) + \( \frac{-7}{17} \)
a = -\(\frac{3}{17}\)x - \(\frac{7}{17}\)

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

5a² + 3a² = 8a²