Question

The volume of a cube is given by the expression below . What is the expression for the side length of the cube?
the expression is 27x^3+8y^3+54x^2+36xy^2​

Answer 1

Answer:

a = 3x+2y

Step-by-step explanation:

volume of cube = 27x^3+8y^3+54x^2+36y^2

volume of cube is in the form of (a+b)^3.

(3x)^3+(2y)^3+3(3x)^2(2y)+3(3x)(2y)^2 = (3x+2y)^3.

There fore, a^3 = (3x+2y)^3.

(Here, a = length of cube).

There fore, a = 3x+2y

Hope it helps you..

Answer 2

Each side of cube is (3x+2y) units.

Given:

• Volume of a cube as a polynomial expression.
• $27 {x}^{3} + 8 {y}^{3} + 54{x}^{2}y + 36x {y}^{2}$

To find:

• Side of cube.

Solution:

Formula/identity to be used:

1. Volume of cube= side³
2. ${(a + b)}^{ 3} = {a}^{3} + {b}^{3} + 3a {b}^{2} + 3 {a}^{2} b$

Step 1:

Rewrite the polynomial of volume so that identity can be applied.

$27 {x}^{3} + 8 {y}^{3} + 54{x}^{2}y + 36x {y}^{2} = {(3x)}^{3} + {(2y)}^{3} + 3(3{x})^{2}(2y) + 3(3x) {(2y)}^{2}$

it is clear that

$( {3x + 2y)}^{3} = {(3x)}^{3} + {(2y)}^{3} + 3(3{x})^{2}(2y) + 3(3x) {(2y)}^{2}$

as on comparison from identity

$a = 3x \\ b = 2y$

Step 2:

Volume polynomial can be written as

$27 {x}^{3} + 8 {y}^{3} + 54{x}^{2}y + 36x {y}^{2} = ( {3x + 2y)}^{3}$

Now,

We know that

Volume of cube is side³.

Thus,

$\bf {side}^{3} = ( {3x + 2y)}^{3}$

Thus,

Each side of cube is (3x+2y) units.

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