Find the Expanded Form (x+2)^2+(y+5)^2=9

${(x + 2)}^{2} + {(y + 5)}^{2} = 9$

Step 1

Simplify the left side ${(x + 2)}^{2} + {(y + 5)}^{2}$ .

Simplify each term.

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

$(x + 2) (x + 2) + {(y + 5)}^{2} = 9$

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

Apply the distributive property.

$x (x + 2) + 2 (x + 2) + {(y + 5)}^{2} = 9$

Apply the distributive property.

$x \cdot x + x \cdot 2 + 2 (x + 2) + {(y + 5)}^{2} = 9$

Apply the distributive property.

$x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2 + {(y + 5)}^{2} = 9$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 2 + 2 x + 2 \cdot 2 + {(y + 5)}^{2} = 9$

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

$x^{2} + 2 \cdot x + 2 x + 2 \cdot 2 + {(y + 5)}^{2} = 9$

Multiply $2$ by $2$ .

$x^{2} + 2 x + 2 x + 4 + {(y + 5)}^{2} = 9$

Add $2 x$ and $2 x$ .

$x^{2} + 4 x + 4 + {(y + 5)}^{2} = 9$

Rewrite ${(y + 5)}^{2}$ as $(y + 5) (y + 5)$ .

$x^{2} + 4 x + 4 + (y + 5) (y + 5) = 9$

Expand $(y + 5) (y + 5)$ using the FOIL Method.

Apply the distributive property.

$x^{2} + 4 x + 4 + y (y + 5) + 5 (y + 5) = 9$

Apply the distributive property.

$x^{2} + 4 x + 4 + y \cdot y + y \cdot 5 + 5 (y + 5) = 9$

Apply the distributive property.

$x^{2} + 4 x + 4 + y \cdot y + y \cdot 5 + 5 y + 5 \cdot 5 = 9$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} + 4 x + 4 + y^{2} + y \cdot 5 + 5 y + 5 \cdot 5 = 9$

Move $5$ to the left of $y$ .

$x^{2} + 4 x + 4 + y^{2} + 5 \cdot y + 5 y + 5 \cdot 5 = 9$

Multiply $5$ by $5$ .

$x^{2} + 4 x + 4 + y^{2} + 5 y + 5 y + 25 = 9$

Add $5 y$ and $5 y$ .

$x^{2} + 4 x + 4 + y^{2} + 10 y + 25 = 9$

Simplify the expression.

Add $4$ and $25$ .

$x^{2} + 4 x + y^{2} + 10 y + 29 = 9$

Move $4 x$ .

$x^{2} + y^{2} + 4 x + 10 y + 29 = 9$

Step 2

Subtract $9$ from both sides of the equation.

$x^{2} + y^{2} + 4 x + 10 y + 29 - 9 = 0$

Step 3

Subtract $9$ from $29$ .

$x^{2} + y^{2} + 4 x + 10 y + 20 = 0$

Find the Expanded Form (x+2)^2+(y+5)^2=9

Related Questions

Support LCMGCF.com by disabling your adblocker.