Find the Expanded Form (x-1)^2+(y-2)^2=9

${(x - 1)}^{2} + {(y - 2)}^{2} = 9$

Step 1

Simplify the left side ${(x - 1)}^{2} + {(y - 2)}^{2}$ .

Simplify each term.

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$(x - 1) (x - 1) + {(y - 2)}^{2} = 9$

Expand $(x - 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$x (x - 1) - 1 (x - 1) + {(y - 2)}^{2} = 9$

Apply the distributive property.

$x \cdot x + x \cdot - 1 - 1 (x - 1) + {(y - 2)}^{2} = 9$

Apply the distributive property.

$x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1 + {(y - 2)}^{2} = 9$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1 + {(y - 2)}^{2} = 9$

Move $- 1$ to the left of $x$ .

$x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1 + {(y - 2)}^{2} = 9$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - 1 x - 1 \cdot - 1 + {(y - 2)}^{2} = 9$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - x - 1 \cdot - 1 + {(y - 2)}^{2} = 9$

Multiply $- 1$ by $- 1$ .

$x^{2} - x - x + 1 + {(y - 2)}^{2} = 9$

Subtract $x$ from $- x$ .

$x^{2} - 2 x + 1 + {(y - 2)}^{2} = 9$

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

$x^{2} - 2 x + 1 + (y - 2) (y - 2) = 9$

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

Apply the distributive property.

$x^{2} - 2 x + 1 + y (y - 2) - 2 (y - 2) = 9$

Apply the distributive property.

$x^{2} - 2 x + 1 + y \cdot y + y \cdot - 2 - 2 (y - 2) = 9$

Apply the distributive property.

$x^{2} - 2 x + 1 + y \cdot y + y \cdot - 2 - 2 y - 2 \cdot - 2 = 9$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} - 2 x + 1 + y^{2} + y \cdot - 2 - 2 y - 2 \cdot - 2 = 9$

Move $- 2$ to the left of $y$ .

$x^{2} - 2 x + 1 + y^{2} - 2 \cdot y - 2 y - 2 \cdot - 2 = 9$

Multiply $- 2$ by $- 2$ .

$x^{2} - 2 x + 1 + y^{2} - 2 y - 2 y + 4 = 9$

Subtract $2 y$ from $- 2 y$ .

$x^{2} - 2 x + 1 + y^{2} - 4 y + 4 = 9$

Simplify the expression.

Add $1$ and $4$ .

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

Move $- 2 x$ .

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

Step 2

Subtract $9$ from both sides of the equation.

$x^{2} + y^{2} - 2 x - 4 y + 5 - 9 = 0$

Step 3

Subtract $9$ from $5$ .

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

Find the Expanded Form (x-1)^2+(y-2)^2=9

Related Questions

Support LCMGCF.com by disabling your adblocker.