Basic Math Examples

$(7 x + 6 y) (7 x - 6 y)$

Step 1

Expand $(7 x + 6 y) (7 x - 6 y)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 x (7 x - 6 y) + 6 y (7 x - 6 y)$

Step 1.2

Apply the distributive property.

$7 x (7 x) + 7 x (- 6 y) + 6 y (7 x - 6 y)$

Step 1.3

Apply the distributive property.

$7 x (7 x) + 7 x (- 6 y) + 6 y (7 x) + 6 y (- 6 y)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $7 x (7 x) + 7 x (- 6 y) + 6 y (7 x) + 6 y (- 6 y)$ .

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Step 2.1.1

Reorder the factors in the terms $7 x (- 6 y)$ and $6 y (7 x)$ .

$7 x (7 x) - 6 \cdot 7 x y + 6 \cdot 7 x y + 6 y (- 6 y)$

Step 2.1.2

Add $- 6 \cdot 7 x y$ and $6 \cdot 7 x y$ .

$7 x (7 x) + 0 + 6 y (- 6 y)$

Step 2.1.3

Add $7 x (7 x)$ and $0$ .

$7 x (7 x) + 6 y (- 6 y)$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$7 \cdot 7 x \cdot x + 6 y (- 6 y)$

Step 2.2.2

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

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Step 2.2.2.1

Move $x$ .

$7 \cdot 7 (x \cdot x) + 6 y (- 6 y)$

Step 2.2.2.2

Multiply $x$ by $x$ .

$7 \cdot 7 x^{2} + 6 y (- 6 y)$

Step 2.2.3

Multiply $7$ by $7$ .

$49 x^{2} + 6 y (- 6 y)$

Step 2.2.4

Rewrite using the commutative property of multiplication.

$49 x^{2} + 6 \cdot - 6 y \cdot y$

Step 2.2.5

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

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Step 2.2.5.1

Move $y$ .

$49 x^{2} + 6 \cdot - 6 (y \cdot y)$

Step 2.2.5.2

Multiply $y$ by $y$ .

$49 x^{2} + 6 \cdot - 6 y^{2}$

Step 2.2.6

Multiply $6$ by $- 6$ .

$49 x^{2} - 36 y^{2}$