a cube with side length $5h^{2}$ is stacked on another cube with side length $3k$. what is the total volume…

a cube with side length $5h^{2}$ is stacked on another cube with side length $3k$. what is the total volume of the cubes in factored form?\n$(5h^{2})^{3}+(3k)^{3}$\n$(5h^{2}+3k)(25h^{4}-15h^{2}k + 9k^{2})$\n$(5h^{2}+3k)(25h^{4}+15h^{2}k + 9k^{2})$\n$(5h^{2}+3k)^{3}$

a cube with side length $5h^{2}$ is stacked on another cube with side length $3k$. what is the total volume of the cubes in factored form?\n$(5h^{2})^{3}+(3k)^{3}$\n$(5h^{2}+3k)(25h^{4}-15h^{2}k + 9k^{2})$\n$(5h^{2}+3k)(25h^{4}+15h^{2}k + 9k^{2})$\n$(5h^{2}+3k)^{3}$

Answer

Explanation:

Step1: Recall volume formula for cube

The volume of a cube with side - length $a$ is $V = a^{3}$. For the first cube with side - length $5h^{2}$, its volume $V_1=(5h^{2})^{3}=125h^{6}$. For the second cube with side - length $3k$, its volume $V_2=(3k)^{3}=27k^{3}$. The total volume $V = V_1+V_2=(5h^{2})^{3}+(3k)^{3}$.

Step2: Apply sum - of - cubes formula

The sum - of - cubes formula is $a^{3}+b^{3}=(a + b)(a^{2}-ab + b^{2})$. Here, $a = 5h^{2}$ and $b = 3k$. So, $(5h^{2})^{3}+(3k)^{3}=(5h^{2}+3k)[(5h^{2})^{2}-(5h^{2})\times(3k)+(3k)^{2}]$.

Step3: Simplify the expression

$(5h^{2}+3k)[(5h^{2})^{2}-(5h^{2})\times(3k)+(3k)^{2}]=(5h^{2}+3k)(25h^{4}-15h^{2}k + 9k^{2})$.

Answer:

$(5h^{2}+3k)(25h^{4}-15h^{2}k + 9k^{2})$