Basic Math Examples

$c^{2} + \frac{4}{3} c + \frac{4}{9}$

Step 1

Rewrite the middle term.

$c^{2} + 2 c \frac{2}{3} + 0 + \frac{4}{9}$

Step 2

Rearrange terms.

$c^{2} + 2 c \frac{2}{3} + \frac{4}{9} + 0$

Step 3

Factor first three terms by perfect square rule.

${(c + \frac{2}{3})}^{2} + 0$

Step 4

Rewrite ${(c + \frac{2}{3})}^{2}$ as $(c + \frac{2}{3}) (c + \frac{2}{3})$ .

$(c + \frac{2}{3}) (c + \frac{2}{3}) + 0$

Step 5

Expand $(c + \frac{2}{3}) (c + \frac{2}{3})$ using the FOIL Method.

Tap for more steps...

Step 5.1

Apply the distributive property.

$c (c + \frac{2}{3}) + \frac{2}{3} (c + \frac{2}{3}) + 0$

Step 5.2

Apply the distributive property.

$c \cdot c + c \frac{2}{3} + \frac{2}{3} (c + \frac{2}{3}) + 0$

Step 5.3

Apply the distributive property.

$c \cdot c + c \frac{2}{3} + \frac{2}{3} c + \frac{2}{3} \cdot \frac{2}{3} + 0$

Step 6

Simplify and combine like terms.

Tap for more steps...

Step 6.1

Simplify each term.

Tap for more steps...

Step 6.1.1

Multiply $c$ by $c$ .

$c^{2} + c \frac{2}{3} + \frac{2}{3} c + \frac{2}{3} \cdot \frac{2}{3} + 0$

Step 6.1.2

Combine $c$ and $\frac{2}{3}$ .

$c^{2} + \frac{c \cdot 2}{3} + \frac{2}{3} c + \frac{2}{3} \cdot \frac{2}{3} + 0$

Step 6.1.3

Move $2$ to the left of $c$ .

$c^{2} + \frac{2 \cdot c}{3} + \frac{2}{3} c + \frac{2}{3} \cdot \frac{2}{3} + 0$

Step 6.1.4

Multiply $2$ by $c$ .

$c^{2} + \frac{2 c}{3} + \frac{2}{3} c + \frac{2}{3} \cdot \frac{2}{3} + 0$

Step 6.1.5

Combine $\frac{2}{3}$ and $c$ .

$c^{2} + \frac{2 c}{3} + \frac{2 c}{3} + \frac{2}{3} \cdot \frac{2}{3} + 0$

Step 6.1.6

Multiply $\frac{2}{3} \cdot \frac{2}{3}$ .

Tap for more steps...

Step 6.1.6.1

Multiply $\frac{2}{3}$ by $\frac{2}{3}$ .

$c^{2} + \frac{2 c}{3} + \frac{2 c}{3} + \frac{2 \cdot 2}{3 \cdot 3} + 0$

Step 6.1.6.2

Multiply $2$ by $2$ .

$c^{2} + \frac{2 c}{3} + \frac{2 c}{3} + \frac{4}{3 \cdot 3} + 0$

Step 6.1.6.3

Multiply $3$ by $3$ .

$c^{2} + \frac{2 c}{3} + \frac{2 c}{3} + \frac{4}{9} + 0$

Step 6.2

Add $\frac{2 c}{3}$ and $\frac{2 c}{3}$ .

$c^{2} + 2 \frac{2 c}{3} + \frac{4}{9} + 0$

Step 7

Multiply $2 \frac{2 c}{3}$ .

Tap for more steps...

Step 7.1

Combine $2$ and $\frac{2 c}{3}$ .

$c^{2} + \frac{2 (2 c)}{3} + \frac{4}{9} + 0$

Step 7.2

Multiply $2$ by $2$ .

$c^{2} + \frac{4 c}{3} + \frac{4}{9} + 0$

Step 8

Add $c^{2} + \frac{4 c}{3} + \frac{4}{9}$ and $0$ .

$c^{2} + \frac{4 c}{3} + \frac{4}{9}$

Step 9

Factor using the perfect square rule.

Tap for more steps...

Step 9.1

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

$c^{2} + \frac{4 c}{3} + \frac{2^{2}}{9}$

Step 9.2

Rewrite $9$ as $3^{2}$ .

$c^{2} + \frac{4 c}{3} + \frac{2^{2}}{3^{2}}$

Step 9.3

Rewrite $\frac{2^{2}}{3^{2}}$ as ${(\frac{2}{3})}^{2}$ .

$c^{2} + \frac{4 c}{3} + {(\frac{2}{3})}^{2}$

Step 9.4

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

$\frac{4 c}{3} = 2 \cdot c \cdot \frac{2}{3}$

Step 9.5

Rewrite the polynomial.

$c^{2} + 2 \cdot c \cdot \frac{2}{3} + {(\frac{2}{3})}^{2}$

Step 9.6

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = c$ and $b = \frac{2}{3}$ .

${(c + \frac{2}{3})}^{2}$