Find the Perfect Square Trinomial (x-9)(3x-9)

$(x - 9) (3 x - 9)$

Step 1

Expand $(x - 9) (3 x - 9)$ using the FOIL Method.

Apply the distributive property.

$x (3 x - 9) - 9 (3 x - 9)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $- 9$ to the left of $x$ .

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

Multiply $3$ by $- 9$ .

$3 x^{2} - 9 x - 27 x - 9 \cdot - 9$

Multiply $- 9$ by $- 9$ .

$3 x^{2} - 9 x - 27 x + 81$

Subtract $27 x$ from $- 9 x$ .

$3 x^{2} - 36 x + 81$