Expand the Trigonometric Expression (3x-2y)^2

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

Step 1

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

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

Step 2

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

Apply the distributive property.

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

Apply the distributive property.

$3 x (3 x) + 3 x (- 2 y) - 2 y (3 x - 2 y)$

Apply the distributive property.

$3 x (3 x) + 3 x (- 2 y) - 2 y (3 x) - 2 y (- 2 y)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $3$ by $- 2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 2$ by $3$ .

$9 x^{2} - 6 x y - 6 y x - 2 y (- 2 y)$

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $- 2$ by $- 2$ .

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

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

Move $y$ .

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

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

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

Expand the Trigonometric Expression (3x-2y)^2

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