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 x 2b = (8 x 2) (a x b) = 16ab

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 7 x 8) + (2 x 8 x 5) + (2 x 7 x 5)
sa = (112) + (80) + (70)
sa = 262

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 -32 as well and sum (Inside, Outside) to equal 4. For this problem, those two numbers are -4 and 8. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² + 4y - 32
y² + (-4 + 8)y + (-4 x 8)
(y - 4)(y + 8)

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.