Trigonometry Examples

$(3 + 4 x) (3 - 4 x)$

Step 1

Expand

$(3 + 4 x) (3 - 4 x)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 (3 - 4 x) + 4 x (3 - 4 x)$

Step 1.2

Apply the distributive property.

$3 \cdot 3 + 3 (- 4 x) + 4 x (3 - 4 x)$

Step 1.3

Apply the distributive property.

$3 \cdot 3 + 3 (- 4 x) + 4 x \cdot 3 + 4 x (- 4 x)$

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

$3$ by

$3$ .

$9 + 3 (- 4 x) + 4 x \cdot 3 + 4 x (- 4 x)$

Step 2.1.2

Multiply

$- 4$ by

$3$ .

$9 - 12 x + 4 x \cdot 3 + 4 x (- 4 x)$

Step 2.1.3

Multiply

$3$ by

$4$ .

$9 - 12 x + 12 x + 4 x (- 4 x)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$9 - 12 x + 12 x + 4 \cdot - 4 x \cdot x$

Step 2.1.5

Multiply

$x$ by

$x$ by adding the exponents.

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Step 2.1.5.1

Move

$x$ .

$9 - 12 x + 12 x + 4 \cdot - 4 (x \cdot x)$

Step 2.1.5.2

Multiply

$x$ by

$x$ .

$9 - 12 x + 12 x + 4 \cdot - 4 x^{2}$

Step 2.1.6

Multiply

$4$ by

$- 4$ .

$9 - 12 x + 12 x - 16 x^{2}$

Step 2.2

Add

$- 12 x$ and

$12 x$ .

$9 + 0 - 16 x^{2}$

Step 2.3

Add

$9$ and

$0$ .

$9 - 16 x^{2}$