question factor $q^{3}+1$ completely. answer attempt 1 out of 2
question factor $q^{3}+1$ completely. answer attempt 1 out of 2
Answer
Explanation:
Step1: Recall sum - of - cubes formula
The sum - of - cubes formula is $a^{3}+b^{3}=(a + b)(a^{2}-ab + b^{2})$. In the expression $q^{3}+1$, we have $a = q$ and $b = 1$.
Step2: Apply the formula
Substitute $a = q$ and $b = 1$ into the sum - of - cubes formula: $(q + 1)(q^{2}-q\times1+1^{2})=(q + 1)(q^{2}-q + 1)$
Answer:
$(q + 1)(q^{2}-q + 1)$