The side length, s, of a cube is 3x 2y. If V = s3, what is the volume of the cube? 3x3 18x2y 36xy2 8y3 27x3 54x2y 18xy2 2y3 27x3

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2 years ago

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18x2y 12xy2 2y3 27x3 54x2y 36xy2 8y3.

1 answer:

uranmaximum [27] · Answer 1 · 2023-03-03T00:56:07+03:00

The volume of the cube is 27x³ + 8y³ +54x²y + 36xy².

<h2>Volume of cube </h2>

The volume of a cube is the cube of its side.

$\rm{ Volume\ of\ cube = (side)^3$

<h2>Given to us</h2>

<h3>Algebraic Identity</h3>

$(a+b)^3= a^3 +b^3 +3a^2b+3ab^2$

<h3>The volume of the cube</h3>

$\begin{aligned}Volume &= s^3\\&= (3x+2y)^3\end{aligned}$

Applying algebraic Identity,

$=(3x+2y)^3\\\\ =(3x)^3+(2y)^3+[3\times (3y)^2 \times2y]+[3 \times 3x \times(2y)^2]\\\\= 27x^3 + 8y^3 +54x^2y +36xy^2$

Hence, the volume of the cube is 27x³ + 8y³ +54x²y + 36xy².

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