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

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

Step 1

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

Simplify each term.

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

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

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

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

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

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

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

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

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

Multiply $- 1$ by $- 1$ .

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

Subtract $x$ from $- x$ .

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

Rewrite ${(y + 1)}^{2}$ as $(y + 1) (y + 1)$ .

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

Expand $(y + 1) (y + 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

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

Multiply $y$ by $1$ .

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

Multiply $y$ by $1$ .

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

Multiply $1$ by $1$ .

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

Add $y$ and $y$ .

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

Simplify the expression.

Add $1$ and $1$ .

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

Move $- 2 x$ .

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

Step 2

Subtract $9$ from both sides of the equation.

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

Step 3

Subtract $9$ from $2$ .

$x^{2} + y^{2} - 2 x + 2 y - 7 = 0$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.