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.

3a x 8b = (3 x 8) (a x b) = 24ab

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 4 x 5) + (2 x 5 x 5) + (2 x 4 x 5)
sa = (40) + (50) + (40)
sa = 130

You need to find the value of a so solve the first equation in terms of x:

9a + x = 3
x = 3 - 9a

then substitute the result (3 - 9a) into the second equation:

-5a + 9(3 - 9a) = -4
-5a + (9 x 3) + (9 x -9a) = -4
-5a + 27 - 81a = -4
-5a - 81a = -4 - 27
-86a = -31
a = \( \frac{-31}{-86} \)
a = \(\frac{31}{86}\)

A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.

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\( \sqrt{2} \)