Find the Product (6x-3y)^2

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

Step 1

Rewrite ${(6 x - 3 y)}^{2}$ as $(6 x - 3 y) (6 x - 3 y)$ .

$(6 x - 3 y) (6 x - 3 y)$

Step 2

Expand $(6 x - 3 y) (6 x - 3 y)$ using the FOIL Method.

Apply the distributive property.

$6 x (6 x - 3 y) - 3 y (6 x - 3 y)$

Apply the distributive property.

$6 x (6 x) + 6 x (- 3 y) - 3 y (6 x - 3 y)$

Apply the distributive property.

$6 x (6 x) + 6 x (- 3 y) - 3 y (6 x) - 3 y (- 3 y)$

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$6 \cdot 6 x \cdot x + 6 x (- 3 y) - 3 y (6 x) - 3 y (- 3 y)$

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

Move $x$ .

$6 \cdot 6 (x \cdot x) + 6 x (- 3 y) - 3 y (6 x) - 3 y (- 3 y)$

Multiply $x$ by $x$ .

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

Multiply $6$ by $6$ .

$36 x^{2} + 6 x (- 3 y) - 3 y (6 x) - 3 y (- 3 y)$

Rewrite using the commutative property of multiplication.

$36 x^{2} + 6 \cdot - 3 x y - 3 y (6 x) - 3 y (- 3 y)$

Multiply $6$ by $- 3$ .

$36 x^{2} - 18 x y - 3 y (6 x) - 3 y (- 3 y)$

Rewrite using the commutative property of multiplication.

$36 x^{2} - 18 x y - 3 \cdot 6 y x - 3 y (- 3 y)$

Multiply $- 3$ by $6$ .

$36 x^{2} - 18 x y - 18 y x - 3 y (- 3 y)$

Rewrite using the commutative property of multiplication.

$36 x^{2} - 18 x y - 18 y x - 3 \cdot - 3 y \cdot y$

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

Move $y$ .

$36 x^{2} - 18 x y - 18 y x - 3 \cdot - 3 (y \cdot y)$

Multiply $y$ by $y$ .

$36 x^{2} - 18 x y - 18 y x - 3 \cdot - 3 y^{2}$

Multiply $- 3$ by $- 3$ .

$36 x^{2} - 18 x y - 18 y x + 9 y^{2}$

Subtract $18 y x$ from $- 18 x y$ .

Move $y$ .

$36 x^{2} - 18 x y - 18 x y + 9 y^{2}$

Subtract $18 x y$ from $- 18 x y$ .

$36 x^{2} - 36 x y + 9 y^{2}$

Find the Product (6x-3y)^2

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