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.

6a x 7b = (6 x 7) (a x b) = 42ab

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 = \( \sqrt{a} \) = \( \sqrt{4} \) = 2

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 = 2² + 2²
c² = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)

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.

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

-7z - 7 > \( \frac{z}{-1} \)
-1 x (-7z - 7) > z
(-1 x -7z) + (-1 x -7) > z
7z + 7 > z
7z + 7 - z > 0
7z - z > -7
6z > -7
z > \( \frac{-7}{6} \)
z > -1\(\frac{1}{6}\)

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.