Given the function $q(x)=x^{3}$ , which of the following is equivalent to $q(2 x+a)+q(x)$
?
A) $8 x^{3}+a^{3}$

B) $9 x^{3}+a^{3}$

C) $8 x^{3}+12 x^{2} a+6 x a^{2}+a^{3}$

D) $9 x^{3}+12 x^{2} a+6 x a^{2}+a^{3}$

Question

Given the function $q(x)=x^{3}$ , which of the following is equivalent to $q(2 x+a)+q(x)$
 ?
A) $8 x^{3}+a^{3}$

B) $9 x^{3}+a^{3}$

C) $8 x^{3}+12 x^{2} a+6 x a^{2}+a^{3}$

D) $9 x^{3}+12 x^{2} a+6 x a^{2}+a^{3}$

Quizplus · Accepted Answer

To find the equivalent expression for $q(2x+a)+q(x)$, we substitute $2x+a$ and $x$ into the given function $q(x)=x^3$. This gives us $(2x+a)^3 + x^3$. Expanding $(2x+a)^3$ results in $8x^3 + 12x^2a + 6xa^2 + a^3$, and adding $x^3$ to this gives $9x^3 + 12x^2a + 6xa^2 + a^3$, which matches option D.

Given the Function q(x)=x3q(x)=x^{3}q(x)=x3 , Which of the Following Is Equivalent To

Given the Function $q(x)=x^{3}$ , Which of the Following Is Equivalent To