Basic Math Examples

$y z^{2} - y^{3} + z^{3} - y^{2} z$

Step 1

Factor out the greatest common factor from each group.

Tap for more steps...

Step 1.1

Group the first two terms and the last two terms.

$(y z^{2} - y^{3}) + z^{3} - y^{2} z$

Step 1.2

Factor out the greatest common factor (GCF) from each group.

$y (z^{2} - y^{2}) + z (z^{2} - y^{2})$

Step 2

Factor the polynomial by factoring out the greatest common factor, $z^{2} - y^{2}$ .

$(z^{2} - y^{2}) (y + z)$

Step 3

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = z$ and $b = y$ .

$(z + y) (z - y) (y + z)$

Step 4

Combine exponents.

Tap for more steps...

Step 4.1

Reorder terms.

$(y + z) (z - y) (y + z)$

Step 4.2

Raise $y + z$ to the power of $1$ .

${(y + z)}^{1} (y + z) (z - y)$

Step 4.3

Raise $y + z$ to the power of $1$ .

${(y + z)}^{1} {(y + z)}^{1} (z - y)$

Step 4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(y + z)}^{1 + 1} (z - y)$

Step 4.5

Add $1$ and $1$ .

${(y + z)}^{2} (z - y)$