Maths-
General
Easy

Question

# The length of each side of a cube is 14𝑥 + 8 𝑓𝑒𝑒𝑡. Write a polynomial in standard form to represent the volume of the cube.

Hint:

## The correct answer is: 512 feet3.

### The length of each side of a cube is 14x + 8 feet.Volume of the cube = (14x + 8)3 = (14x + 8)2(14x + 8) (14x + 8)2 = (14x + 8)(14x + 8)= 14x(14x + 8) + 8(14x + 8)= 14x(14x) + 14x(8) + 8(14x) + 8(8)= 196 x2 + 112x + 112x + 64= 196 x2 + 224x + 64Now, we need to find (196 x2 + 224x + 64)(14x + 8)(196 x2 + 224x + 64)(14x + 8) = 196x2(14x + 8) + 224x(14x + 8) + 64(14x + 8)= 196x2(14x) + 196x2(8) + 224x(14x) + 224x(8) + 64(14x) + 64(8)= 2744x3 + 1568x2 + 3136x2 + 1792x + 896x + 512= 2744x3 + 4704x2 + 2688x + 512Volume of the cube = (14x + 8)3 = 2744x3 + 4704x2 + 2688x + 512 feet3Final Answer: Hence, the polynomial which represents the volume of the cube of 14x + 8 feet side is 2744x3 + 4704x2 + 2688x + 512 feet3.

This question can be easily solved by using the formula
(a + b)3 = a3 + 3a2b + 3ab2 + b3