Algebra Examples

$(2 x - y) (x + 5 y)$

Step 1

Expand $(2 x - y) (x + 5 y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$2 x (x + 5 y) - y (x + 5 y)$

Step 1.2

Apply the distributive property.

$2 x \cdot x + 2 x (5 y) - y (x + 5 y)$

Step 1.3

Apply the distributive property.

$2 x \cdot x + 2 x (5 y) - y x - y (5 y)$

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

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

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Step 2.1.1.1

Move $x$ .

$2 (x \cdot x) + 2 x (5 y) - y x - y (5 y)$

Step 2.1.1.2

Multiply $x$ by $x$ .

$2 x^{2} + 2 x (5 y) - y x - y (5 y)$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$2 x^{2} + 2 \cdot 5 x y - y x - y (5 y)$

Step 2.1.3

Multiply $2$ by $5$ .

$2 x^{2} + 10 x y - y x - y (5 y)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$2 x^{2} + 10 x y - y x - 1 \cdot 5 y \cdot y$

Step 2.1.5

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

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Step 2.1.5.1

Move $y$ .

$2 x^{2} + 10 x y - y x - 1 \cdot 5 (y \cdot y)$

Step 2.1.5.2

Multiply $y$ by $y$ .

$2 x^{2} + 10 x y - y x - 1 \cdot 5 y^{2}$

Step 2.1.6

Multiply $- 1$ by $5$ .

$2 x^{2} + 10 x y - y x - 5 y^{2}$

Step 2.2

Subtract $y x$ from $10 x y$ .

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Step 2.2.1

Move $y$ .

$2 x^{2} + 10 x y - 1 x y - 5 y^{2}$

Step 2.2.2

Subtract $x y$ from $10 x y$ .

$2 x^{2} + 9 x y - 5 y^{2}$