the side length, s, of a cube is 3x + 2y. if v = s³, what is the volume of the cube?\n3x³ + 18x²y + 36xy² +…

Explanation:

Step1: Expand $(3x + 2y)^3$ using the formula $(a + b)^3=a^{3}+3a^{2}b + 3ab^{2}+b^{3}$

Here $a = 3x$ and $b=2y$. $(3x)^{3}+3\times(3x)^{2}\times(2y)+3\times(3x)\times(2y)^{2}+(2y)^{3}$

Step2: Calculate each term

$(3x)^{3}=27x^{3}$, $3\times(3x)^{2}\times(2y)=3\times9x^{2}\times2y = 54x^{2}y$, $3\times(3x)\times(2y)^{2}=3\times3x\times4y^{2}=36xy^{2}$, $(2y)^{3}=8y^{3}$

Step3: Combine the terms

$27x^{3}+54x^{2}y + 36xy^{2}+8y^{3}$

Answer:

$27x^{3}+54x^{2}y + 36xy^{2}+8y^{3}$