Simplify ((3x-2)^6)/((3x-2)^4)

$\frac{{(3 x - 2)}^{6}}{{(3 x - 2)}^{4}}$

Step 1

Reduce the expression by cancelling the common factors.

Cancel the common factor of ${(3 x - 2)}^{6}$ and ${(3 x - 2)}^{4}$ .

Factor ${(3 x - 2)}^{4}$ out of ${(3 x - 2)}^{6}$ .

$\frac{{(3 x - 2)}^{4} {(3 x - 2)}^{2}}{{(3 x - 2)}^{4}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{{(3 x - 2)}^{4} {(3 x - 2)}^{2}}{{(3 x - 2)}^{4} \cdot 1}$

Cancel the common factor.

$\frac{{(3 x - 2)}^{4} {(3 x - 2)}^{2}}{{(3 x - 2)}^{4} \cdot 1}$

Rewrite the expression.

$\frac{{(3 x - 2)}^{2}}{1}$

Divide ${(3 x - 2)}^{2}$ by $1$ .

${(3 x - 2)}^{2}$

Rewrite ${(3 x - 2)}^{2}$ as $(3 x - 2) (3 x - 2)$ .

$(3 x - 2) (3 x - 2)$

Step 2

Expand $(3 x - 2) (3 x - 2)$ using the FOIL Method.

Apply the distributive property.

$3 x (3 x - 2) - 2 (3 x - 2)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot - 2 - 2 (3 x - 2)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

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

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

$9 x^{2} + 3 x \cdot - 2 - 2 (3 x) - 2 \cdot - 2$

Multiply $- 2$ by $3$ .

$9 x^{2} - 6 x - 2 (3 x) - 2 \cdot - 2$

Multiply $3$ by $- 2$ .

$9 x^{2} - 6 x - 6 x - 2 \cdot - 2$

Multiply $- 2$ by $- 2$ .

$9 x^{2} - 6 x - 6 x + 4$

Subtract $6 x$ from $- 6 x$ .

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