Algebra Examples

$(3 x + y) (3 x - y)$

Step 1

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

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Step 1.1

Apply the distributive property.

$3 x (3 x - y) + y (3 x - y)$

Step 1.2

Apply the distributive property.

$3 x (3 x) + 3 x (- y) + y (3 x - y)$

Step 1.3

Apply the distributive property.

$3 x (3 x) + 3 x (- y) + y (3 x) + y (- y)$

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.

$3 \cdot 3 x \cdot x + 3 x (- y) + y (3 x) + y (- y)$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x (- y) + y (3 x) + y (- y)$

Step 2.1.2.2

Multiply $x$ by $x$ .

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

Step 2.1.3

Multiply $3$ by $3$ .

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

$9 x^{2} + 3 \cdot - 1 x y + y (3 x) + y (- y)$

Step 2.1.5

Multiply $3$ by $- 1$ .

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

Step 2.1.6

Rewrite using the commutative property of multiplication.

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

Step 2.1.7

Rewrite using the commutative property of multiplication.

$9 x^{2} - 3 x y + 3 y x - y \cdot y$

Step 2.1.8

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

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Step 2.1.8.1

Move $y$ .

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

Step 2.1.8.2

Multiply $y$ by $y$ .

$9 x^{2} - 3 x y + 3 y x - y^{2}$

Step 2.2

Add $- 3 x y$ and $3 y x$ .

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Step 2.2.1

Move $y$ .

$9 x^{2} - 3 x y + 3 x y - y^{2}$

Step 2.2.2

Add $- 3 x y$ and $3 x y$ .

$9 x^{2} + 0 - y^{2}$

Step 2.3

Add $9 x^{2}$ and $0$ .

$9 x^{2} - y^{2}$