Basic Math Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Rewrite using the commutative property of multiplication.

$y^{3} + 3 \cdot 2 y^{2} z + 3 y {(2 z)}^{2} + {(2 z)}^{3}$

Step 2.2

Multiply $3$ by $2$ .

$y^{3} + 6 y^{2} z + 3 y {(2 z)}^{2} + {(2 z)}^{3}$

Step 2.3

Apply the product rule to $2 z$ .

$y^{3} + 6 y^{2} z + 3 y (2^{2} z^{2}) + {(2 z)}^{3}$

Step 2.4

Rewrite using the commutative property of multiplication.

$y^{3} + 6 y^{2} z + 3 \cdot 2^{2} y z^{2} + {(2 z)}^{3}$

Step 2.5

Raise $2$ to the power of $2$ .

$y^{3} + 6 y^{2} z + 3 \cdot 4 y z^{2} + {(2 z)}^{3}$

Step 2.6

Multiply $3$ by $4$ .

$y^{3} + 6 y^{2} z + 12 y z^{2} + {(2 z)}^{3}$

Step 2.7

Apply the product rule to $2 z$ .

$y^{3} + 6 y^{2} z + 12 y z^{2} + 2^{3} z^{3}$

Step 2.8

Raise $2$ to the power of $3$ .

$y^{3} + 6 y^{2} z + 12 y z^{2} + 8 z^{3}$