Chemistry Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $x \cdot x + x (5 y) - 5 y x - 5 y (5 y)$ .

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Step 2.1.1

Reorder the factors in the terms $x (5 y)$ and $- 5 y x$ .

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

Step 2.1.2

Subtract $5 x y$ from $5 x y$ .

$x \cdot x + 0 - 5 y (5 y)$

Step 2.1.3

Add $x \cdot x$ and $0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x$ by $x$ .

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

Step 2.2.2

Rewrite using the commutative property of multiplication.

$x^{2} - 5 \cdot 5 y \cdot y$

Step 2.2.3

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

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Step 2.2.3.1

Move $y$ .

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

Step 2.2.3.2

Multiply $y$ by $y$ .

$x^{2} - 5 \cdot 5 y^{2}$

Step 2.2.4

Multiply $- 5$ by $5$ .

$x^{2} - 25 y^{2}$