Factor the sum or difference of two cubes.
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D) prime

Question

Quizplus · Accepted Answer

The formula for factoring the sum of two cubes is: 
a³ + b³ = (a + b)(a² – ab + b²)
In this case, we have 11ebb63d_1b76 and b851 as our two cubes, so:
(11ebb63d_1b76)³ + (b851)³ = (11ebb63d_1b76 + b851)(11ebb63d_1b76² – 11ebb63d_1b76b851 + b851²)
Simplifying the second set of parentheses gives us: 
(11ebb63d_1b76)² + (11ebb63d_1b76)(b851) + (b851)² = 11ebb63d_1b76_4ce2_b851_dbf348482178_TB8475_11 The sum of two cubes of the form $a^3+b^3$ factors into $(a+b)(a^2-ab+b^2)$, so we can see that in the expression $11ebb63d_1b76_25d0_b851_b366d54ecd37_TB8475_11$, the first two groups of digits represent $a$ and $b$ (in some order). Taking the difference of two cubes of the form $a^3-b^3$ factors into $(a-b)(a^2+ab+b^2)$, so we can see that $25d0$ represents $a^3$ and $b^3$ must be $b^{3}=20^{3}=8000$. Now we can factor $a^{3}-b^{3}$ using the quadratic formula, which yields $a^3=11ebb63d_1b76_4ce2_b851_dbf348482178$ and $b^{3}=8000$. Thus, the factored form is $(a-b)(a^2+ab+b^2)=(a-20)(a^{2}+20a+400)$. Since $a$ is a large prime number, we cannot factor further. Therefore, the best choice is $\boxed{	extbf{(B)}\ 11ebb63d_1b76_4ce2_b851_dbf348482178_TB8475_11}$.

Factor the Sum or Difference of Two Cubes