Multiply mentally
-$(5 p-1)\left(25 p^{2}+5 p+1\right)$
A) $125 p^{3}+1$
B) $25 p^{3}-1$
C) $125 p^{3}-1$
D) $125 p^{3}+30 p^{2}-1$

Question

Quizplus · Accepted Answer

This is a product of a binomial and a trinomial. When you multiply $(5p-1)$ by $(25p^2 + 5p + 1)$, you apply the distributive property (also known as the FOIL method for binomials, extended to trinomials). The multiplication results in $125p^3 + 25p^2 + 5p - 25p^2 - 5p - 1$. Notice that $+25p^2$ and $-25p^2$ cancel each other out, as do $+5p$ and $-5p$, leaving $125p^3 - 1$.

Multiply Mentally - (5p−1)(25p2+5p+1)(5 p-1)\left(25 p^{2}+5 p+1\right)(5p−1)(25p2+5p+1) A) 125p3+1125 p^{3}+1125p3+1 B) 25p3−125 p^{3}-125p3−1

Multiply Mentally
- $(5 p-1)\left(25 p^{2}+5 p+1\right)$ A) $125 p^{3}+1$ B) $25 p^{3}-1$