Expand the Trigonometric Expression (6x+1)(1-3x)

$(6 x + 1) (1 - 3 x)$

Step 1

Expand $(6 x + 1) (1 - 3 x)$ using the FOIL Method.

Apply the distributive property.

$6 x (1 - 3 x) + 1 (1 - 3 x)$

Apply the distributive property.

$6 x \cdot 1 + 6 x (- 3 x) + 1 (1 - 3 x)$

Apply the distributive property.

$6 x \cdot 1 + 6 x (- 3 x) + 1 \cdot 1 + 1 (- 3 x)$

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $6$ by $1$ .

$6 x + 6 x (- 3 x) + 1 \cdot 1 + 1 (- 3 x)$

Rewrite using the commutative property of multiplication.

$6 x + 6 \cdot - 3 x \cdot x + 1 \cdot 1 + 1 (- 3 x)$

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

Move $x$ .

$6 x + 6 \cdot - 3 (x \cdot x) + 1 \cdot 1 + 1 (- 3 x)$

Multiply $x$ by $x$ .

$6 x + 6 \cdot - 3 x^{2} + 1 \cdot 1 + 1 (- 3 x)$

Multiply $6$ by $- 3$ .

$6 x - 18 x^{2} + 1 \cdot 1 + 1 (- 3 x)$

Multiply $1$ by $1$ .

$6 x - 18 x^{2} + 1 + 1 (- 3 x)$

Multiply $- 3 x$ by $1$ .

$6 x - 18 x^{2} + 1 - 3 x$

Subtract $3 x$ from $6 x$ .

$3 x - 18 x^{2} + 1$