Find the Expanded Form (x-3)^2+(y+4)^2=5^2

${(x - 3)}^{2} + {(y + 4)}^{2} = 5^{2}$

Step 1

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

Simplify each term.

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

$(x - 3) (x - 3) + {(y + 4)}^{2} = 5^{2}$

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

Apply the distributive property.

$x (x - 3) - 3 (x - 3) + {(y + 4)}^{2} = 5^{2}$

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 (x - 3) + {(y + 4)}^{2} = 5^{2}$

Apply the distributive property.

$x \cdot x + x \cdot - 3 - 3 x - 3 \cdot - 3 + {(y + 4)}^{2} = 5^{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 3 - 3 x - 3 \cdot - 3 + {(y + 4)}^{2} = 5^{2}$

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

$x^{2} - 3 \cdot x - 3 x - 3 \cdot - 3 + {(y + 4)}^{2} = 5^{2}$

Multiply $- 3$ by $- 3$ .

$x^{2} - 3 x - 3 x + 9 + {(y + 4)}^{2} = 5^{2}$

Subtract $3 x$ from $- 3 x$ .

$x^{2} - 6 x + 9 + {(y + 4)}^{2} = 5^{2}$

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

$x^{2} - 6 x + 9 + (y + 4) (y + 4) = 5^{2}$

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

Apply the distributive property.

$x^{2} - 6 x + 9 + y (y + 4) + 4 (y + 4) = 5^{2}$

Apply the distributive property.

$x^{2} - 6 x + 9 + y \cdot y + y \cdot 4 + 4 (y + 4) = 5^{2}$

Apply the distributive property.

$x^{2} - 6 x + 9 + y \cdot y + y \cdot 4 + 4 y + 4 \cdot 4 = 5^{2}$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 6 x + 9 + y^{2} + y \cdot 4 + 4 y + 4 \cdot 4 = 5^{2}$

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

$x^{2} - 6 x + 9 + y^{2} + 4 \cdot y + 4 y + 4 \cdot 4 = 5^{2}$

Multiply $4$ by $4$ .

$x^{2} - 6 x + 9 + y^{2} + 4 y + 4 y + 16 = 5^{2}$

Add $4 y$ and $4 y$ .

$x^{2} - 6 x + 9 + y^{2} + 8 y + 16 = 5^{2}$

Simplify the expression.

Add $9$ and $16$ .

$x^{2} - 6 x + y^{2} + 8 y + 25 = 5^{2}$

Move $- 6 x$ .

$x^{2} + y^{2} - 6 x + 8 y + 25 = 5^{2}$

Step 2

Raise $5$ to the power of $2$ .

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

Step 3

Subtract $25$ from both sides of the equation.

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

Step 4

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=5^2

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