Basic Math Examples

$v^{2} + 5 v + \frac{25}{4}$

Step 1

Rewrite $25$ as $5^{2}$ .

$v^{2} + 5 v + \frac{5^{2}}{4}$

Step 2

Rewrite $4$ as $2^{2}$ .

$v^{2} + 5 v + \frac{5^{2}}{2^{2}}$

Step 3

Rewrite $\frac{5^{2}}{2^{2}}$ as ${(\frac{5}{2})}^{2}$ .

$v^{2} + 5 v + {(\frac{5}{2})}^{2}$

Step 4

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$5 v = 2 \cdot v \cdot \frac{5}{2}$

Step 5

Rewrite the polynomial.

$v^{2} + 2 \cdot v \cdot \frac{5}{2} + {(\frac{5}{2})}^{2}$

Step 6

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = v$ and $b = \frac{5}{2}$ .

${(v + \frac{5}{2})}^{2}$