select the correct answer.\nwhat is the factored form of $b^{3}-1,000$?\na. $(b + 10)(b^{2}-10b + 100)$\nb…

select the correct answer.\nwhat is the factored form of $b^{3}-1,000$?\na. $(b + 10)(b^{2}-10b + 100)$\nb. $(b - 10)(b^{2}+10b + 100)$\nc. $(b - 10)(10b^{2}+b + 100)$\nd. $(b + 10)(10b^{2}-b + 100)$

select the correct answer.\nwhat is the factored form of $b^{3}-1,000$?\na. $(b + 10)(b^{2}-10b + 100)$\nb. $(b - 10)(b^{2}+10b + 100)$\nc. $(b - 10)(10b^{2}+b + 100)$\nd. $(b + 10)(10b^{2}-b + 100)$

Answer

Explanation:

Step1: Recall the difference - of - cubes formula

The difference - of - cubes formula is $a^{3}-b^{3}=(a - b)(a^{2}+ab + b^{2})$. In the expression $b^{3}-1000$, we have $a = b$ and $b = 10$ since $1000=10^{3}$.

Step2: Apply the formula

Substitute $a = b$ and $b = 10$ into the formula $a^{3}-b^{3}=(a - b)(a^{2}+ab + b^{2})$. We get $b^{3}-10^{3}=(b - 10)(b^{2}+10b + 100)$.

Answer:

B. $(b - 10)(b^{2}+10b + 100)$