Algebra Examples

${(x + 7)}^{2} + y^{2} = 81$

Simplify the left side ${(x + 7)}^{2} + y^{2}$ .

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Simplify each term.

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Rewrite ${(x + 7)}^{2}$ as $(x + 7) (x + 7)$ .

$(x + 7) (x + 7) + y^{2} = 81$

Expand $(x + 7) (x + 7)$ using the FOIL Method.

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Apply the distributive property.

$x (x + 7) + 7 (x + 7) + y^{2} = 81$

Apply the distributive property.

$x x + x \cdot 7 + 7 (x + 7) + y^{2} = 81$

Apply the distributive property.

$x x + x \cdot 7 + (7 x + 7 \cdot 7) + y^{2} = 81$

Remove parentheses.

$x x + x \cdot 7 + 7 x + 7 \cdot 7 + y^{2} = 81$

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ by adding the exponents.

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Combine $x$ and $x$

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Raise $x$ to the power of $1$ .

$x x + x \cdot 7 + 7 x + 7 \cdot 7 + y^{2} = 81$

Raise $x$ to the power of $1$ .

$x x + x \cdot 7 + 7 x + 7 \cdot 7 + y^{2} = 81$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{1 + 1} + x \cdot 7 + 7 x + 7 \cdot 7 + y^{2} = 81$

Add $1$ and $1$ .

$x^{2} + x \cdot 7 + 7 x + 7 \cdot 7 + y^{2} = 81$

Move $7$ to the left of the expression $x \cdot 7$ .

$x^{2} + 7 \cdot x + 7 x + 7 \cdot 7 + y^{2} = 81$

Multiply $7$ by $x$ .

$x^{2} + 7 x + 7 x + 7 \cdot 7 + y^{2} = 81$

Multiply $7$ by $7$ .

$x^{2} + 7 x + 7 x + 49 + y^{2} = 81$

Add $7 x$ and $7 x$ .

$x^{2} + 14 x + 49 + y^{2} = 81$

Reorder.

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Move $49$ .

$x^{2} + 14 x + y^{2} + 49 = 81$

Move $14 x$ .

$x^{2} + y^{2} + 14 x + 49 = 81$

Move $81$ to the left side of the equation by subtracting it from both sides.

$x^{2} + y^{2} + 14 x + 49 - 81 = 0$

Subtract $81$ from $49$ .

$x^{2} + y^{2} + 14 x - 32 = 0$

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