Find the Product (3x-y)^2

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

Step 1

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

$(3 x - y) (3 x - y)$

Step 2

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

Apply the distributive property.

$3 x (3 x - y) - y (3 x - y)$

Apply the distributive property.

$3 x (3 x) + 3 x (- y) - y (3 x - y)$

Apply the distributive property.

$3 x (3 x) + 3 x (- y) - y (3 x) - y (- y)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

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

Rewrite using the commutative property of multiplication.

$9 x^{2} + 3 \cdot - 1 x y - y (3 x) - y (- y)$

Multiply $3$ by $- 1$ .

$9 x^{2} - 3 x y - y (3 x) - y (- y)$

Rewrite using the commutative property of multiplication.

$9 x^{2} - 3 x y - 1 \cdot 3 y x - y (- y)$

Multiply $- 1$ by $3$ .

$9 x^{2} - 3 x y - 3 y x - y (- y)$

Rewrite using the commutative property of multiplication.

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

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$9 x^{2} - 3 x y - 3 y x - 1 \cdot - 1 (y \cdot y)$

Multiply $y$ by $y$ .

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

Multiply $- 1$ by $- 1$ .

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

Multiply $y^{2}$ by $1$ .

$9 x^{2} - 3 x y - 3 y x + y^{2}$

Subtract $3 y x$ from $- 3 x y$ .

Move $y$ .

$9 x^{2} - 3 x y - 3 x y + y^{2}$

Subtract $3 x y$ from $- 3 x y$ .

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

Find the Product (3x-y)^2

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