Precalculus Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify terms.

Tap for more steps...

Step 2.1

Simplify each term.

Tap for more steps...

Step 2.1.1

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

$3 (8 + 3 \cdot 2^{2} y + 3 \cdot 2 y^{2} + y^{3})$

Step 2.1.2

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

$3 (8 + 3 \cdot 4 y + 3 \cdot 2 y^{2} + y^{3})$

Step 2.1.3

Multiply $3$ by $4$ .

$3 (8 + 12 y + 3 \cdot 2 y^{2} + y^{3})$

Step 2.1.4

Multiply $3$ by $2$ .

$3 (8 + 12 y + 6 y^{2} + y^{3})$

Step 2.2

Apply the distributive property.

$3 \cdot 8 + 3 (12 y) + 3 (6 y^{2}) + 3 y^{3}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

Multiply $3$ by $8$ .

$24 + 3 (12 y) + 3 (6 y^{2}) + 3 y^{3}$

Step 3.2

Multiply $12$ by $3$ .

$24 + 36 y + 3 (6 y^{2}) + 3 y^{3}$

Step 3.3

Multiply $6$ by $3$ .

$24 + 36 y + 18 y^{2} + 3 y^{3}$