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

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

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $3$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $3$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $3$ by $3$ .

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

Add $6 x y$ and $6 y x$ .

Move $y$ .

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

Add $6 x y$ and $6 x y$ .

$4 x^{2} + 12 x y + 9 y^{2} + {(2 x - 3 y)}^{2}$

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

$4 x^{2} + 12 x y + 9 y^{2} + (2 x - 3 y) (2 x - 3 y)$

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

Apply the distributive property.

$4 x^{2} + 12 x y + 9 y^{2} + 2 x (2 x - 3 y) - 3 y (2 x - 3 y)$

Apply the distributive property.

$4 x^{2} + 12 x y + 9 y^{2} + 2 x (2 x) + 2 x (- 3 y) - 3 y (2 x - 3 y)$

Apply the distributive property.

$4 x^{2} + 12 x y + 9 y^{2} + 2 x (2 x) + 2 x (- 3 y) - 3 y (2 x) - 3 y (- 3 y)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 x^{2} + 12 x y + 9 y^{2} + 2 \cdot 2 x \cdot x + 2 x (- 3 y) - 3 y (2 x) - 3 y (- 3 y)$

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

Move $x$ .

$4 x^{2} + 12 x y + 9 y^{2} + 2 \cdot 2 (x \cdot x) + 2 x (- 3 y) - 3 y (2 x) - 3 y (- 3 y)$

Multiply $x$ by $x$ .

$4 x^{2} + 12 x y + 9 y^{2} + 2 \cdot 2 x^{2} + 2 x (- 3 y) - 3 y (2 x) - 3 y (- 3 y)$

Multiply $2$ by $2$ .

$4 x^{2} + 12 x y + 9 y^{2} + 4 x^{2} + 2 x (- 3 y) - 3 y (2 x) - 3 y (- 3 y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} + 12 x y + 9 y^{2} + 4 x^{2} + 2 \cdot - 3 x y - 3 y (2 x) - 3 y (- 3 y)$

Multiply $2$ by $- 3$ .

$4 x^{2} + 12 x y + 9 y^{2} + 4 x^{2} - 6 x y - 3 y (2 x) - 3 y (- 3 y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} + 12 x y + 9 y^{2} + 4 x^{2} - 6 x y - 3 \cdot 2 y x - 3 y (- 3 y)$

Multiply $- 3$ by $2$ .

$4 x^{2} + 12 x y + 9 y^{2} + 4 x^{2} - 6 x y - 6 y x - 3 y (- 3 y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} + 12 x y + 9 y^{2} + 4 x^{2} - 6 x y - 6 y x - 3 \cdot - 3 y \cdot y$

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

Move $y$ .

$4 x^{2} + 12 x y + 9 y^{2} + 4 x^{2} - 6 x y - 6 y x - 3 \cdot - 3 (y \cdot y)$

Multiply $y$ by $y$ .

$4 x^{2} + 12 x y + 9 y^{2} + 4 x^{2} - 6 x y - 6 y x - 3 \cdot - 3 y^{2}$

Multiply $- 3$ by $- 3$ .

$4 x^{2} + 12 x y + 9 y^{2} + 4 x^{2} - 6 x y - 6 y x + 9 y^{2}$

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

Move $y$ .

$4 x^{2} + 12 x y + 9 y^{2} + 4 x^{2} - 6 x y - 6 x y + 9 y^{2}$

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

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

Simplify by adding terms.

Combine the opposite terms in $4 x^{2} + 12 x y + 9 y^{2} + 4 x^{2} - 12 x y + 9 y^{2}$ .

Subtract $12 x y$ from $12 x y$ .

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

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

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

Add $4 x^{2}$ and $4 x^{2}$ .

$8 x^{2} + 9 y^{2} + 9 y^{2}$

Add $9 y^{2}$ and $9 y^{2}$ .

$8 x^{2} + 18 y^{2}$

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

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