Finite Math Examples

${(x + 10)}^{2} + {(y + 12)}^{2}$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(x + 10)}^{2}$ as $(x + 10) (x + 10)$ .

$(x + 10) (x + 10) + {(y + 12)}^{2}$

Step 1.2

Expand $(x + 10) (x + 10)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$x (x + 10) + 10 (x + 10) + {(y + 12)}^{2}$

Step 1.2.2

Apply the distributive property.

$x \cdot x + x \cdot 10 + 10 (x + 10) + {(y + 12)}^{2}$

Step 1.2.3

Apply the distributive property.

$x \cdot x + x \cdot 10 + 10 x + 10 \cdot 10 + {(y + 12)}^{2}$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 10 + 10 x + 10 \cdot 10 + {(y + 12)}^{2}$

Step 1.3.1.2

Move $10$ to the left of $x$ .

$x^{2} + 10 \cdot x + 10 x + 10 \cdot 10 + {(y + 12)}^{2}$

Step 1.3.1.3

Multiply $10$ by $10$ .

$x^{2} + 10 x + 10 x + 100 + {(y + 12)}^{2}$

Step 1.3.2

Add $10 x$ and $10 x$ .

$x^{2} + 20 x + 100 + {(y + 12)}^{2}$

Step 1.4

Rewrite ${(y + 12)}^{2}$ as $(y + 12) (y + 12)$ .

$x^{2} + 20 x + 100 + (y + 12) (y + 12)$

Step 1.5

Expand $(y + 12) (y + 12)$ using the FOIL Method.

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Step 1.5.1

Apply the distributive property.

$x^{2} + 20 x + 100 + y (y + 12) + 12 (y + 12)$

Step 1.5.2

Apply the distributive property.

$x^{2} + 20 x + 100 + y \cdot y + y \cdot 12 + 12 (y + 12)$

Step 1.5.3

Apply the distributive property.

$x^{2} + 20 x + 100 + y \cdot y + y \cdot 12 + 12 y + 12 \cdot 12$

Step 1.6

Simplify and combine like terms.

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Step 1.6.1

Simplify each term.

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Step 1.6.1.1

Multiply $y$ by $y$ .

$x^{2} + 20 x + 100 + y^{2} + y \cdot 12 + 12 y + 12 \cdot 12$

Step 1.6.1.2

Move $12$ to the left of $y$ .

$x^{2} + 20 x + 100 + y^{2} + 12 \cdot y + 12 y + 12 \cdot 12$

Step 1.6.1.3

Multiply $12$ by $12$ .

$x^{2} + 20 x + 100 + y^{2} + 12 y + 12 y + 144$

Step 1.6.2

Add $12 y$ and $12 y$ .

$x^{2} + 20 x + 100 + y^{2} + 24 y + 144$

Step 2

Simplify the expression.

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Step 2.1

Add $100$ and $144$ .

$x^{2} + 20 x + y^{2} + 24 y + 244$

Step 2.2

Move $20 x$ .

$x^{2} + y^{2} + 20 x + 24 y + 244$