Factor the difference of two squares. $v ^ { 2 } - \frac { 81 } { 4 }$
A) $\left( v + \frac { 9 } { 2 } \right) ^ { 2 }$
B) $\left( v - \frac { 9 } { 2 } \right) ^ { 2 }$
C) $\left( v + \frac { 2 } { 9 } \right) ^ { 2 }$
D) $\left( v + \frac { 9 } { 2 } \right) \left( v - \frac { 9 } { 2 } \right)$
E) $\left( v + \frac { 2 } { 9 } \right) \left( v - \frac { 2 } { 9 } \right)$

Question

Quizplus · Accepted Answer

The difference of two squares formula is $(a^2-b^2)=(a+b)(a-b)$. In this case, $a=v$ and $b=\frac{9}{2}$ since $\left(\frac{9}{2}\right)^2=\frac{81}{4}$. Therefore, applying the formula, we get $$(v^2-\frac{81}{4})=(v+\frac{9}{2})(v-\frac{9}{2})$$ which is equivalent to choice D.

Factor the Difference of Two Squares v2−814v ^ { 2 } - \frac { 81 } { 4 }v2−481​

Factor the Difference of Two Squares $v ^ { 2 } - \frac { 81 } { 4 }$