Pre-Algebra Examples

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

Step 1

Use the Binomial Theorem.

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

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $3 x$ .

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

Step 2.2

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

$27 x^{3} + 3 {(3 x)}^{2} (2 y) + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.3

Rewrite using the commutative property of multiplication.

$27 x^{3} + 3 \cdot 2 {(3 x)}^{2} y + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.4

Multiply $3$ by $2$ .

$27 x^{3} + 6 {(3 x)}^{2} y + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.5

Apply the product rule to $3 x$ .

$27 x^{3} + 6 (3^{2} x^{2}) y + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.6

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

$27 x^{3} + 6 (9 x^{2}) y + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.7

Multiply $9$ by $6$ .

$27 x^{3} + 54 x^{2} y + 3 (3 x) {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.8

Multiply $3$ by $3$ .

$27 x^{3} + 54 x^{2} y + 9 x {(2 y)}^{2} + {(2 y)}^{3}$

Step 2.9

Apply the product rule to $2 y$ .

$27 x^{3} + 54 x^{2} y + 9 x (2^{2} y^{2}) + {(2 y)}^{3}$

Step 2.10

Rewrite using the commutative property of multiplication.

$27 x^{3} + 54 x^{2} y + 9 \cdot 2^{2} x y^{2} + {(2 y)}^{3}$

Step 2.11

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

$27 x^{3} + 54 x^{2} y + 9 \cdot 4 x y^{2} + {(2 y)}^{3}$

Step 2.12

Multiply $9$ by $4$ .

$27 x^{3} + 54 x^{2} y + 36 x y^{2} + {(2 y)}^{3}$

Step 2.13

Apply the product rule to $2 y$ .

$27 x^{3} + 54 x^{2} y + 36 x y^{2} + 2^{3} y^{3}$

Step 2.14

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

$27 x^{3} + 54 x^{2} y + 36 x y^{2} + 8 y^{3}$