Basic Math Examples

$(2 a + 3 y) (2 a - 3 y)$

Step 1

Expand $(2 a + 3 y) (2 a - 3 y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 a (2 a - 3 y) + 3 y (2 a - 3 y)$

Step 1.2

Apply the distributive property.

$2 a (2 a) + 2 a (- 3 y) + 3 y (2 a - 3 y)$

Step 1.3

Apply the distributive property.

$2 a (2 a) + 2 a (- 3 y) + 3 y (2 a) + 3 y (- 3 y)$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a \cdot a + 2 a (- 3 y) + 3 y (2 a) + 3 y (- 3 y)$

Step 2.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 2.1.2.1

Move $a$ .

$2 \cdot 2 (a \cdot a) + 2 a (- 3 y) + 3 y (2 a) + 3 y (- 3 y)$

Step 2.1.2.2

Multiply $a$ by $a$ .

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

Step 2.1.3

Multiply $2$ by $2$ .

$4 a^{2} + 2 a (- 3 y) + 3 y (2 a) + 3 y (- 3 y)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

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

Step 2.1.5

Multiply $2$ by $- 3$ .

$4 a^{2} - 6 a y + 3 y (2 a) + 3 y (- 3 y)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

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

Step 2.1.7

Multiply $3$ by $2$ .

$4 a^{2} - 6 a y + 6 y a + 3 y (- 3 y)$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$4 a^{2} - 6 a y + 6 y a + 3 \cdot - 3 y \cdot y$

Step 2.1.9

Multiply $y$ by $y$ by adding the exponents.

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Step 2.1.9.1

Move $y$ .

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

Step 2.1.9.2

Multiply $y$ by $y$ .

$4 a^{2} - 6 a y + 6 y a + 3 \cdot - 3 y^{2}$

Step 2.1.10

Multiply $3$ by $- 3$ .

$4 a^{2} - 6 a y + 6 y a - 9 y^{2}$

Step 2.2

Add $- 6 a y$ and $6 y a$ .

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Step 2.2.1

Move $y$ .

$4 a^{2} - 6 a y + 6 a y - 9 y^{2}$

Step 2.2.2

Add $- 6 a y$ and $6 a y$ .

$4 a^{2} + 0 - 9 y^{2}$

Step 2.3

Add $4 a^{2}$ and $0$ .

$4 a^{2} - 9 y^{2}$