Find the Product (1-3ax)(3ax+1)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Multiply $3 a x$ by $1$ .

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

Multiply $1$ by $1$ .

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

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

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

Multiply $a$ by $a$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

$3 a x + 1 - 3 a^{2} x^{2} \cdot 3 - 3 a x \cdot 1$

Multiply $3$ by $- 3$ .

$3 a x + 1 - 9 a^{2} x^{2} - 3 a x \cdot 1$

Multiply $- 3$ by $1$ .

$3 a x + 1 - 9 a^{2} x^{2} - 3 a x$

Subtract $3 a x$ from $3 a x$ .

$1 - 9 a^{2} x^{2} + 0$

Add $1$ and $0$ .

$- 9 a^{2} x^{2} + 1$