Chemistry Examples

$(5 x - 7 y) (5 x + 7 y)$

Step 1

Expand $(5 x - 7 y) (5 x + 7 y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$5 x (5 x + 7 y) - 7 y (5 x + 7 y)$

Step 1.2

Apply the distributive property.

$5 x (5 x) + 5 x (7 y) - 7 y (5 x + 7 y)$

Step 1.3

Apply the distributive property.

$5 x (5 x) + 5 x (7 y) - 7 y (5 x) - 7 y (7 y)$

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.

$5 \cdot 5 x \cdot x + 5 x (7 y) - 7 y (5 x) - 7 y (7 y)$

Step 2.1.2

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

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Step 2.1.2.1

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x (7 y) - 7 y (5 x) - 7 y (7 y)$

Step 2.1.2.2

Multiply $x$ by $x$ .

$5 \cdot 5 x^{2} + 5 x (7 y) - 7 y (5 x) - 7 y (7 y)$

Step 2.1.3

Multiply $5$ by $5$ .

$25 x^{2} + 5 x (7 y) - 7 y (5 x) - 7 y (7 y)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$25 x^{2} + 5 \cdot 7 x y - 7 y (5 x) - 7 y (7 y)$

Step 2.1.5

Multiply $5$ by $7$ .

$25 x^{2} + 35 x y - 7 y (5 x) - 7 y (7 y)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$25 x^{2} + 35 x y - 7 \cdot 5 y x - 7 y (7 y)$

Step 2.1.7

Multiply $- 7$ by $5$ .

$25 x^{2} + 35 x y - 35 y x - 7 y (7 y)$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$25 x^{2} + 35 x y - 35 y x - 7 \cdot 7 y \cdot y$

Step 2.1.9

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

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Step 2.1.9.1

Move $y$ .

$25 x^{2} + 35 x y - 35 y x - 7 \cdot 7 (y \cdot y)$

Step 2.1.9.2

Multiply $y$ by $y$ .

$25 x^{2} + 35 x y - 35 y x - 7 \cdot 7 y^{2}$

Step 2.1.10

Multiply $- 7$ by $7$ .

$25 x^{2} + 35 x y - 35 y x - 49 y^{2}$

Step 2.2

Subtract $35 y x$ from $35 x y$ .

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Step 2.2.1

Move $y$ .

$25 x^{2} + 35 x y - 35 x y - 49 y^{2}$

Step 2.2.2

Subtract $35 x y$ from $35 x y$ .

$25 x^{2} + 0 - 49 y^{2}$

Step 2.3

Add $25 x^{2}$ and $0$ .

$25 x^{2} - 49 y^{2}$