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 x^{2} + 112x + 112x + 64

= 196 x^{2} + 224x + 64

Now, we need to find (196 x^{2} + 224x + 64)(14x + 8)

(196 x^{2} + 224x + 64)(14x + 8) = 196x^{2}(14x + 8) + 224x(14x + 8) + 64(14x + 8)

= 196x^{2}(14x) + 196x^{2}(8) + 224x(14x) + 224x(8) + 64(14x) + 64(8)

= 2744x^{3} + 1568x^{2} + 3136x^{2} + 1792x + 896x + 512

= 2744x^{3} + 4704x^{2} + 2688x + 512

Volume of the cube = (14x + 8)^{3} = 2744x^{3} + 4704x^{2} + 2688x + 512 feet^{3}

Final Answer:

Hence, the polynomial which represents the volume of the cube of 14x + 8 feet side is 2744x^{3} + 4704x^{2} + 2688x + 512 feet^{3}.

^{2}= (14x + 8)(14x + 8)

^{2}+ 112x + 112x + 64

^{2}+ 224x + 64

Now, we need to find (196 x

^{2}+ 224x + 64)(14x + 8)

^{2}+ 224x + 64)(14x + 8) = 196x

^{2}(14x + 8) + 224x(14x + 8) + 64(14x + 8)

^{2}(14x) + 196x

^{2}(8) + 224x(14x) + 224x(8) + 64(14x) + 64(8)

^{3}+ 1568x

^{2}+ 3136x

^{2}+ 1792x + 896x + 512

^{3}+ 4704x

^{2}+ 2688x + 512

^{3}= 2744x

^{3}+ 4704x

^{2}+ 2688x + 512 feet

^{3}

Final Answer:

Hence, the polynomial which represents the volume of the cube of 14x + 8 feet side is 2744x

^{3}+ 4704x

^{2}+ 2688x + 512 feet

^{3}.

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