Basic Math Examples

$\frac{5 {(a + h)}^{3} - 6 {(a + h)}^{2} - 5 a^{2} - 6 a^{2}}{h}$

Step 1

Use the Binomial Theorem.

$\frac{5 (a^{3} + 3 a^{2} h + 3 a h^{2} + h^{3}) - 6 {(a + h)}^{2} - 5 a^{2} - 6 a^{2}}{h}$

Step 2

Apply the distributive property.

$\frac{5 a^{3} + 5 (3 a^{2} h) + 5 (3 a h^{2}) + 5 h^{3} - 6 {(a + h)}^{2} - 5 a^{2} - 6 a^{2}}{h}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Multiply $3$ by $5$ .

$\frac{5 a^{3} + 15 (a^{2} h) + 5 (3 a h^{2}) + 5 h^{3} - 6 {(a + h)}^{2} - 5 a^{2} - 6 a^{2}}{h}$

Step 3.2

Multiply $3$ by $5$ .

$\frac{5 a^{3} + 15 (a^{2} h) + 15 (a h^{2}) + 5 h^{3} - 6 {(a + h)}^{2} - 5 a^{2} - 6 a^{2}}{h}$

Step 4

Remove parentheses.

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 6 {(a + h)}^{2} - 5 a^{2} - 6 a^{2}}{h}$

Step 5

Rewrite ${(a + h)}^{2}$ as $(a + h) (a + h)$ .

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 6 ((a + h) (a + h)) - 5 a^{2} - 6 a^{2}}{h}$

Step 6

Expand $(a + h) (a + h)$ using the FOIL Method.

Tap for more steps...

Step 6.1

Apply the distributive property.

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 6 (a (a + h) + h (a + h)) - 5 a^{2} - 6 a^{2}}{h}$

Step 6.2

Apply the distributive property.

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 6 (a \cdot a + a h + h (a + h)) - 5 a^{2} - 6 a^{2}}{h}$

Step 6.3

Apply the distributive property.

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 6 (a \cdot a + a h + h a + h \cdot h) - 5 a^{2} - 6 a^{2}}{h}$

Step 7

Simplify and combine like terms.

Tap for more steps...

Step 7.1

Simplify each term.

Tap for more steps...

Step 7.1.1

Multiply $a$ by $a$ .

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 6 (a^{2} + a h + h a + h \cdot h) - 5 a^{2} - 6 a^{2}}{h}$

Step 7.1.2

Multiply $h$ by $h$ .

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 6 (a^{2} + a h + h a + h^{2}) - 5 a^{2} - 6 a^{2}}{h}$

Step 7.2

Add $a h$ and $h a$ .

Tap for more steps...

Step 7.2.1

Reorder $h$ and $a$ .

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 6 (a^{2} + a h + a h + h^{2}) - 5 a^{2} - 6 a^{2}}{h}$

Step 7.2.2

Add $a h$ and $a h$ .

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 6 (a^{2} + 2 a h + h^{2}) - 5 a^{2} - 6 a^{2}}{h}$

Step 8

Apply the distributive property.

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 6 a^{2} - 6 (2 a h) - 6 h^{2} - 5 a^{2} - 6 a^{2}}{h}$

Step 9

Multiply $2$ by $- 6$ .

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 6 a^{2} - 12 (a h) - 6 h^{2} - 5 a^{2} - 6 a^{2}}{h}$

Step 10

Subtract $5 a^{2}$ from $- 6 a^{2}$ .

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 11 a^{2} - 12 a h - 6 h^{2} - 6 a^{2}}{h}$

Step 11

Subtract $6 a^{2}$ from $- 11 a^{2}$ .

$\frac{5 a^{3} + 15 a^{2} h + 15 a h^{2} + 5 h^{3} - 17 a^{2} - 12 a h - 6 h^{2}}{h}$