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 methods used to find the product of binomials are called special products.
Multiplying a number by itself is often called squaring.
For example (x + 3)(x + 3) = (x + 3)2
Volume of cube of side a = a3
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 + 64
Now, 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 + 512
Volume of the cube = (14x + 8)3 = 2744x3 + 4704x2 + 2688x + 512 feet3
Final Answer:
Hence, the polynomial which represents the volume of the cube of 14x + 8 feet side is 2744x3 + 4704x2 + 2688x + 512 feet3.
Now, we need to find (196 x2 + 224x + 64)(14x + 8)
Final 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
Related Questions to study
The length of each side of a cube is 14𝑥 + 8 𝑓𝑒𝑒𝑡. Write a polynomial in standard form to represent the surface area of the cube.
This question can be easily solved by using the formula
(a + b)2 = a2 + 2ab + b2
The length of each side of a cube is 14𝑥 + 8 𝑓𝑒𝑒𝑡. Write a polynomial in standard form to represent the surface area of the cube.
This question can be easily solved by using the formula
(a + b)2 = a2 + 2ab + b2
in. and a width of 
in. What is the perimeter of the rectangle
. What expression represents the surface area of the cube?
