Basic Math Examples

$(12 x + y) (12 x - y)$

Step 1

Expand $(12 x + y) (12 x - y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$12 x (12 x - y) + y (12 x - y)$

Step 1.2

Apply the distributive property.

$12 x (12 x) + 12 x (- y) + y (12 x - y)$

Step 1.3

Apply the distributive property.

$12 x (12 x) + 12 x (- y) + y (12 x) + y (- y)$

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.

$12 \cdot 12 x \cdot x + 12 x (- y) + y (12 x) + y (- y)$

Step 2.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.2.1

Move $x$ .

$12 \cdot 12 (x \cdot x) + 12 x (- y) + y (12 x) + y (- y)$

Step 2.1.2.2

Multiply $x$ by $x$ .

$12 \cdot 12 x^{2} + 12 x (- y) + y (12 x) + y (- y)$

Step 2.1.3

Multiply $12$ by $12$ .

$144 x^{2} + 12 x (- y) + y (12 x) + y (- y)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$144 x^{2} + 12 \cdot - 1 x y + y (12 x) + y (- y)$

Step 2.1.5

Multiply $12$ by $- 1$ .

$144 x^{2} - 12 x y + y (12 x) + y (- y)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$144 x^{2} - 12 x y + 12 y x + y (- y)$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$144 x^{2} - 12 x y + 12 y x - y \cdot y$

Step 2.1.8

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

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Step 2.1.8.1

Move $y$ .

$144 x^{2} - 12 x y + 12 y x - (y \cdot y)$

Step 2.1.8.2

Multiply $y$ by $y$ .

$144 x^{2} - 12 x y + 12 y x - y^{2}$

Step 2.2

Add $- 12 x y$ and $12 y x$ .

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Step 2.2.1

Move $y$ .

$144 x^{2} - 12 x y + 12 x y - y^{2}$

Step 2.2.2

Add $- 12 x y$ and $12 x y$ .

$144 x^{2} + 0 - y^{2}$

Step 2.3

Add $144 x^{2}$ and $0$ .

$144 x^{2} - y^{2}$