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.

5a x 5b = (5 x 5) (a x b) = 25ab

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 5. For this problem, those two numbers are 1 and 4. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 5y + 4
y² + (1 + 4)y + (1 x 4)
(y + 1)(y + 4)

The volume of a cylinder is πr²h:

v = πr²h
v = π(7² x 5)
v = 245π

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(5 + 5)(4)
a = ½(10)(4)
a = ½(40) = \( \frac{40}{2} \)
a = 20

Parallel lines are lines that share the same slope (steepness) and therefore never intersect. A transversal occurs when a set of parallel lines are crossed by another line. All of the angles formed by a transversal are called interior angles and angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°) and are called corresponding angles. Alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°) and all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other. Same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°).