Algebra Examples

${(x - 0)}^{2} + {(y - 3)}^{2} = 3^{2}$

Step 1

Simplify each term.

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Step 1.1

Subtract $0$ from $x$ .

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

Apply the distributive property.

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

Step 1.3.2

Apply the distributive property.

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

Step 1.3.3

Apply the distributive property.

$x^{2} + y \cdot y + y \cdot - 3 - 3 y - 3 \cdot - 3 = 3^{2}$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $y$ by $y$ .

$x^{2} + y^{2} + y \cdot - 3 - 3 y - 3 \cdot - 3 = 3^{2}$

Step 1.4.1.2

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

$x^{2} + y^{2} - 3 \cdot y - 3 y - 3 \cdot - 3 = 3^{2}$

Step 1.4.1.3

Multiply $- 3$ by $- 3$ .

$x^{2} + y^{2} - 3 y - 3 y + 9 = 3^{2}$

Step 1.4.2

Subtract $3 y$ from $- 3 y$ .

$x^{2} + y^{2} - 6 y + 9 = 3^{2}$

Step 2

Raise $3$ to the power of $2$ .

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

Step 3

Subtract $9$ from both sides of the equation.

$x^{2} + y^{2} - 6 y + 9 - 9 = 0$

Step 4

Combine the opposite terms in $x^{2} + y^{2} - 6 y + 9 - 9$ .

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Step 4.1

Subtract $9$ from $9$ .

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

Step 4.2

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

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