Basic Math Examples

$a^{2} + n + 2 b^{2} = (a + b) (a + 2 b)$

Step 1

Since $a$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$(a + b) (a + 2 b) = a^{2} + n + 2 b^{2}$

Step 2

Simplify $(a + b) (a + 2 b)$ .

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Step 2.1

Rewrite.

$0 + 0 + (a + b) (a + 2 b) = a^{2} + n + 2 b^{2}$

Step 2.2

Simplify by adding zeros.

$(a + b) (a + 2 b) = a^{2} + n + 2 b^{2}$

Step 2.3

Expand $(a + b) (a + 2 b)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

$a (a + 2 b) + b (a + 2 b) = a^{2} + n + 2 b^{2}$

Step 2.3.2

Apply the distributive property.

$a \cdot a + a (2 b) + b (a + 2 b) = a^{2} + n + 2 b^{2}$

Step 2.3.3

Apply the distributive property.

$a \cdot a + a (2 b) + b a + b (2 b) = a^{2} + n + 2 b^{2}$

Step 2.4

Simplify and combine like terms.

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Step 2.4.1

Simplify each term.

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Step 2.4.1.1

Multiply $a$ by $a$ .

$a^{2} + a (2 b) + b a + b (2 b) = a^{2} + n + 2 b^{2}$

Step 2.4.1.2

Rewrite using the commutative property of multiplication.

$a^{2} + 2 a b + b a + b (2 b) = a^{2} + n + 2 b^{2}$

Step 2.4.1.3

Rewrite using the commutative property of multiplication.

$a^{2} + 2 a b + b a + 2 b \cdot b = a^{2} + n + 2 b^{2}$

Step 2.4.1.4

Multiply $b$ by $b$ by adding the exponents.

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Step 2.4.1.4.1

Move $b$ .

$a^{2} + 2 a b + b a + 2 (b \cdot b) = a^{2} + n + 2 b^{2}$

Step 2.4.1.4.2

Multiply $b$ by $b$ .

$a^{2} + 2 a b + b a + 2 b^{2} = a^{2} + n + 2 b^{2}$

Step 2.4.2

Add $2 a b$ and $b a$ .

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Step 2.4.2.1

Reorder $b$ and $a$ .

$a^{2} + 2 a b + a b + 2 b^{2} = a^{2} + n + 2 b^{2}$

Step 2.4.2.2

Add $2 a b$ and $a b$ .

$a^{2} + 3 a b + 2 b^{2} = a^{2} + n + 2 b^{2}$

Step 3

Move all terms containing $a$ to the left side of the equation.

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Step 3.1

Subtract $a^{2}$ from both sides of the equation.

$a^{2} + 3 a b + 2 b^{2} - a^{2} = n + 2 b^{2}$

Step 3.2

Combine the opposite terms in $a^{2} + 3 a b + 2 b^{2} - a^{2}$ .

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Step 3.2.1

Subtract $a^{2}$ from $a^{2}$ .

$3 a b + 2 b^{2} + 0 = n + 2 b^{2}$

Step 3.2.2

Add $3 a b + 2 b^{2}$ and $0$ .

$3 a b + 2 b^{2} = n + 2 b^{2}$

Step 4

Move all terms not containing $a$ to the right side of the equation.

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Step 4.1

Subtract $2 b^{2}$ from both sides of the equation.

$3 a b = n + 2 b^{2} - 2 b^{2}$

Step 4.2

Combine the opposite terms in $n + 2 b^{2} - 2 b^{2}$ .

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Step 4.2.1

Subtract $2 b^{2}$ from $2 b^{2}$ .

$3 a b = n + 0$

Step 4.2.2

Add $n$ and $0$ .

$3 a b = n$

Step 5

Divide each term in $3 a b = n$ by $3 b$ and simplify.

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Step 5.1

Divide each term in $3 a b = n$ by $3 b$ .

$\frac{3 a b}{3 b} = \frac{n}{3 b}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 a b}{3 b} = \frac{n}{3 b}$

Step 5.2.1.2

Rewrite the expression.

$\frac{a b}{b} = \frac{n}{3 b}$

Step 5.2.2

Cancel the common factor of $b$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{a b}{b} = \frac{n}{3 b}$

Step 5.2.2.2

Divide $a$ by $1$ .

$a = \frac{n}{3 b}$