Find the Expanded Form (x+3)^2+(y+4)^2=25

${(x + 3)}^{2} + {(y + 4)}^{2} = 25$

Step 1

Simplify the left side ${(x + 3)}^{2} + {(y + 4)}^{2}$ .

Simplify each term.

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

$(x + 3) (x + 3) + {(y + 4)}^{2} = 25$

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

Apply the distributive property.

$x (x + 3) + 3 (x + 3) + {(y + 4)}^{2} = 25$

Apply the distributive property.

$x \cdot x + x \cdot 3 + 3 (x + 3) + {(y + 4)}^{2} = 25$

Apply the distributive property.

$x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3 + {(y + 4)}^{2} = 25$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 3 + 3 x + 3 \cdot 3 + {(y + 4)}^{2} = 25$

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

$x^{2} + 3 \cdot x + 3 x + 3 \cdot 3 + {(y + 4)}^{2} = 25$

Multiply $3$ by $3$ .

$x^{2} + 3 x + 3 x + 9 + {(y + 4)}^{2} = 25$

Add $3 x$ and $3 x$ .

$x^{2} + 6 x + 9 + {(y + 4)}^{2} = 25$

Rewrite ${(y + 4)}^{2}$ as $(y + 4) (y + 4)$ .

$x^{2} + 6 x + 9 + (y + 4) (y + 4) = 25$

Expand $(y + 4) (y + 4)$ using the FOIL Method.

Apply the distributive property.

$x^{2} + 6 x + 9 + y (y + 4) + 4 (y + 4) = 25$

Apply the distributive property.

$x^{2} + 6 x + 9 + y \cdot y + y \cdot 4 + 4 (y + 4) = 25$

Apply the distributive property.

$x^{2} + 6 x + 9 + y \cdot y + y \cdot 4 + 4 y + 4 \cdot 4 = 25$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} + 6 x + 9 + y^{2} + y \cdot 4 + 4 y + 4 \cdot 4 = 25$

Move $4$ to the left of $y$ .

$x^{2} + 6 x + 9 + y^{2} + 4 \cdot y + 4 y + 4 \cdot 4 = 25$

Multiply $4$ by $4$ .

$x^{2} + 6 x + 9 + y^{2} + 4 y + 4 y + 16 = 25$

Add $4 y$ and $4 y$ .

$x^{2} + 6 x + 9 + y^{2} + 8 y + 16 = 25$

Simplify the expression.

Add $9$ and $16$ .

$x^{2} + 6 x + y^{2} + 8 y + 25 = 25$

Move $6 x$ .

$x^{2} + y^{2} + 6 x + 8 y + 25 = 25$

Step 2

Subtract $25$ from both sides of the equation.

$x^{2} + y^{2} + 6 x + 8 y + 25 - 25 = 0$

Step 3

Combine the opposite terms in $x^{2} + y^{2} + 6 x + 8 y + 25 - 25$ .

Subtract $25$ from $25$ .

$x^{2} + y^{2} + 6 x + 8 y + 0 = 0$

Add $x^{2} + y^{2} + 6 x + 8 y$ and $0$ .

$x^{2} + y^{2} + 6 x + 8 y = 0$

Find the Expanded Form (x+3)^2+(y+4)^2=25

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