Find the Expanded Form (x+2)^2+(y+3)^2=18

${(x + 2)}^{2} + {(y + 3)}^{2} = 18$

Step 1

Simplify the left side ${(x + 2)}^{2} + {(y + 3)}^{2}$ .

Simplify each term.

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

$(x + 2) (x + 2) + {(y + 3)}^{2} = 18$

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

Apply the distributive property.

$x (x + 2) + 2 (x + 2) + {(y + 3)}^{2} = 18$

Apply the distributive property.

$x \cdot x + x \cdot 2 + 2 (x + 2) + {(y + 3)}^{2} = 18$

Apply the distributive property.

$x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2 + {(y + 3)}^{2} = 18$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 2 + 2 x + 2 \cdot 2 + {(y + 3)}^{2} = 18$

Move $2$ to the left of $x$ .

$x^{2} + 2 \cdot x + 2 x + 2 \cdot 2 + {(y + 3)}^{2} = 18$

Multiply $2$ by $2$ .

$x^{2} + 2 x + 2 x + 4 + {(y + 3)}^{2} = 18$

Add $2 x$ and $2 x$ .

$x^{2} + 4 x + 4 + {(y + 3)}^{2} = 18$

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

$x^{2} + 4 x + 4 + (y + 3) (y + 3) = 18$

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

Apply the distributive property.

$x^{2} + 4 x + 4 + y (y + 3) + 3 (y + 3) = 18$

Apply the distributive property.

$x^{2} + 4 x + 4 + y \cdot y + y \cdot 3 + 3 (y + 3) = 18$

Apply the distributive property.

$x^{2} + 4 x + 4 + y \cdot y + y \cdot 3 + 3 y + 3 \cdot 3 = 18$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} + 4 x + 4 + y^{2} + y \cdot 3 + 3 y + 3 \cdot 3 = 18$

Move $3$ to the left of $y$ .

$x^{2} + 4 x + 4 + y^{2} + 3 \cdot y + 3 y + 3 \cdot 3 = 18$

Multiply $3$ by $3$ .

$x^{2} + 4 x + 4 + y^{2} + 3 y + 3 y + 9 = 18$

Add $3 y$ and $3 y$ .

$x^{2} + 4 x + 4 + y^{2} + 6 y + 9 = 18$

Simplify the expression.

Add $4$ and $9$ .

$x^{2} + 4 x + y^{2} + 6 y + 13 = 18$

Move $4 x$ .

$x^{2} + y^{2} + 4 x + 6 y + 13 = 18$

Step 2

Subtract $18$ from both sides of the equation.

$x^{2} + y^{2} + 4 x + 6 y + 13 - 18 = 0$

Step 3

Subtract $18$ from $13$ .

$x^{2} + y^{2} + 4 x + 6 y - 5 = 0$

Find the Expanded Form (x+2)^2+(y+3)^2=18

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