Find the Expanded Form (x+0.1)^2+(y-0.1)^2=0.5

${(x + 0.1)}^{2} + {(y - 0.1)}^{2} = 0.5$

Step 1

Simplify the left side ${(x + 0.1)}^{2} + {(y - 0.1)}^{2}$ .

Simplify each term.

Rewrite ${(x + 0.1)}^{2}$ as $(x + 0.1) (x + 0.1)$ .

$(x + 0.1) (x + 0.1) + {(y - 0.1)}^{2} = 0.5$

Expand $(x + 0.1) (x + 0.1)$ using the FOIL Method.

Apply the distributive property.

$x (x + 0.1) + 0.1 (x + 0.1) + {(y - 0.1)}^{2} = 0.5$

Apply the distributive property.

$x \cdot x + x \cdot 0.1 + 0.1 (x + 0.1) + {(y - 0.1)}^{2} = 0.5$

Apply the distributive property.

$x \cdot x + x \cdot 0.1 + 0.1 x + 0.1 \cdot 0.1 + {(y - 0.1)}^{2} = 0.5$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot 0.1 + 0.1 x + 0.1 \cdot 0.1 + {(y - 0.1)}^{2} = 0.5$

Move $0.1$ to the left of $x$ .

$x^{2} + 0.1 \cdot x + 0.1 x + 0.1 \cdot 0.1 + {(y - 0.1)}^{2} = 0.5$

Multiply $0.1$ by $0.1$ .

$x^{2} + 0.1 x + 0.1 x + 0.01 + {(y - 0.1)}^{2} = 0.5$

Add $0.1 x$ and $0.1 x$ .

$x^{2} + 0.2 x + 0.01 + {(y - 0.1)}^{2} = 0.5$

Rewrite ${(y - 0.1)}^{2}$ as $(y - 0.1) (y - 0.1)$ .

$x^{2} + 0.2 x + 0.01 + (y - 0.1) (y - 0.1) = 0.5$

Expand $(y - 0.1) (y - 0.1)$ using the FOIL Method.

Apply the distributive property.

$x^{2} + 0.2 x + 0.01 + y (y - 0.1) - 0.1 (y - 0.1) = 0.5$

Apply the distributive property.

$x^{2} + 0.2 x + 0.01 + y \cdot y + y \cdot - 0.1 - 0.1 (y - 0.1) = 0.5$

Apply the distributive property.

$x^{2} + 0.2 x + 0.01 + y \cdot y + y \cdot - 0.1 - 0.1 y - 0.1 \cdot - 0.1 = 0.5$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$x^{2} + 0.2 x + 0.01 + y^{2} + y \cdot - 0.1 - 0.1 y - 0.1 \cdot - 0.1 = 0.5$

Move $- 0.1$ to the left of $y$ .

$x^{2} + 0.2 x + 0.01 + y^{2} - 0.1 \cdot y - 0.1 y - 0.1 \cdot - 0.1 = 0.5$

Multiply $- 0.1$ by $- 0.1$ .

$x^{2} + 0.2 x + 0.01 + y^{2} - 0.1 y - 0.1 y + 0.01 = 0.5$

Subtract $0.1 y$ from $- 0.1 y$ .

$x^{2} + 0.2 x + 0.01 + y^{2} - 0.2 y + 0.01 = 0.5$

Simplify the expression.

Add $0.01$ and $0.01$ .

$x^{2} + 0.2 x + y^{2} - 0.2 y + 0.02 = 0.5$

Move $0.2 x$ .

$x^{2} + y^{2} + 0.2 x - 0.2 y + 0.02 = 0.5$

Step 2

Subtract $0.5$ from both sides of the equation.

$x^{2} + y^{2} + 0.2 x - 0.2 y + 0.02 - 0.5 = 0$

Step 3

Subtract $0.5$ from $0.02$ .

$x^{2} + y^{2} + 0.2 x - 0.2 y - 0.48 = 0$

Find the Expanded Form (x+0.1)^2+(y-0.1)^2=0.5

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