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 -4 as well and sum (Inside, Outside) to equal 0. For this problem, those two numbers are -2 and 2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 4
y² + (-2 + 2)y + (-2 x 2)
(y - 2)(y + 2)

You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a² - a² = 3a² but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.

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

v = h x l x w
v = 7 x 8 x 8
v = 448

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 = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

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 = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)

A cylinder is a solid figure with straight parallel sides and a circular or oval cross section with a radius (r) and a height (h). The volume of a cylinder is π r²h and the surface area is 2(π r²) + 2π rh.