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\frac{25p^{2}-1}{25}
Factor out \frac{1}{25}.
\left(5p-1\right)\left(5p+1\right)
Consider 25p^{2}-1. Rewrite 25p^{2}-1 as \left(5p\right)^{2}-1^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
\frac{\left(5p-1\right)\left(5p+1\right)}{25}
Rewrite the complete factored expression.