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

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

Expand $(3 x + 2 - 3 y) (3 x + 2 + 3 y)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Combine the opposite terms in $3 x (3 x) + 3 x \cdot 2 + 3 x (3 y) + 2 (3 x) + 2 \cdot 2 + 2 (3 y) - 3 y (3 x) - 3 y \cdot 2 - 3 y (3 y)$ .

Reorder the factors in the terms $3 x (3 y)$ and $- 3 y (3 x)$ .

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

Subtract $3 \cdot 3 x y$ from $3 \cdot 3 x y$ .

$3 x (3 x) + 3 x \cdot 2 + 2 (3 x) + 2 \cdot 2 + 2 (3 y) + 0 - 3 y \cdot 2 - 3 y (3 y)$

Add $3 x (3 x) + 3 x \cdot 2 + 2 (3 x) + 2 \cdot 2 + 2 (3 y)$ and $0$ .

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

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

Multiply $2$ by $3$ .

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

Multiply $3$ by $2$ .

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

Multiply $2$ by $2$ .

$9 x^{2} + 6 x + 6 x + 4 + 2 (3 y) - 3 y \cdot 2 - 3 y (3 y)$

Multiply $3$ by $2$ .

$9 x^{2} + 6 x + 6 x + 4 + 6 y - 3 y \cdot 2 - 3 y (3 y)$

Multiply $2$ by $- 3$ .

$9 x^{2} + 6 x + 6 x + 4 + 6 y - 6 y - 3 y (3 y)$

Rewrite using the commutative property of multiplication.

$9 x^{2} + 6 x + 6 x + 4 + 6 y - 6 y - 3 \cdot 3 y \cdot y$

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

Move $y$ .

$9 x^{2} + 6 x + 6 x + 4 + 6 y - 6 y - 3 \cdot 3 (y \cdot y)$

Multiply $y$ by $y$ .

$9 x^{2} + 6 x + 6 x + 4 + 6 y - 6 y - 3 \cdot 3 y^{2}$

Multiply $- 3$ by $3$ .

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

Simplify by adding terms.

Combine the opposite terms in $9 x^{2} + 6 x + 6 x + 4 + 6 y - 6 y - 9 y^{2}$ .

Subtract $6 y$ from $6 y$ .

$9 x^{2} + 6 x + 6 x + 4 + 0 - 9 y^{2}$

Add $9 x^{2} + 6 x + 6 x + 4$ and $0$ .

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

Add $6 x$ and $6 x$ .

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

Reorder.

Move $4$ .

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

Move $12 x$ .

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

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

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