Basic Math Examples

Z^{6} + 1

$Z^{6} + 1$

Step 1

Rewrite

$Z^{6}$ as

${(Z^{2})}^{3}$ .

${(Z^{2})}^{3} + 1$

Step 2

Rewrite

$1$ as

$1^{3}$ .

${(Z^{2})}^{3} + 1^{3}$

Step 3

Since both terms are perfect cubes, factor using the sum of cubes formula,

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ where

$a = Z^{2}$ and

$b = 1$ .

$(Z^{2} + 1) ({(Z^{2})}^{2} - Z^{2} \cdot 1 + 1^{2})$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Multiply the exponents in

${(Z^{2})}^{2}$ .

Tap for more steps...

Step 4.1.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$(Z^{2} + 1) (Z^{2 \cdot 2} - Z^{2} \cdot 1 + 1^{2})$

Step 4.1.2

Multiply

$2$ by

$2$ .

$(Z^{2} + 1) (Z^{4} - Z^{2} \cdot 1 + 1^{2})$

Step 4.2

Multiply

$- 1$ by

$1$ .

$(Z^{2} + 1) (Z^{4} - Z^{2} + 1^{2})$

Step 4.3

One to any power is one.

$(Z^{2} + 1) (Z^{4} - Z^{2} + 1)$