Algebra Examples

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

Step 1

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

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Step 1.1

Rewrite.

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

Step 1.2

Simplify by adding zeros.

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

Step 1.3

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

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Step 1.3.1

Apply the distributive property.

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

Step 1.3.2

Apply the distributive property.

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

Step 1.3.3

Apply the distributive property.

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

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 $a$ by $a$ .

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

Step 1.4.1.2

Rewrite using the commutative property of multiplication.

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

Step 1.4.1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4.1.4

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

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Step 1.4.1.4.1

Move $b$ .

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

Step 1.4.1.4.2

Multiply $b$ by $b$ .

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

Step 1.4.2

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

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Step 1.4.2.1

Reorder $b$ and $a$ .

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

Step 1.4.2.2

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

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

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

Step 2.3.3

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

$n = 3 a b + 0$

Step 2.3.4

Add $3 a b$ and $0$ .

$n = 3 a b$