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\frac{1-98v+2401v^{2}}{49}
Factor out \frac{1}{49}.
\left(49v-1\right)^{2}
Consider 1-98v+2401v^{2}. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=49v and b=1.
\frac{\left(49v-1\right)^{2}}{49}
Rewrite the complete factored expression.