Basic Math Examples

${(a + b)}^{2} - 2 a (a + b)$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(a + b)}^{2}$ as $(a + b) (a + b)$ .

$(a + b) (a + b) - 2 a (a + b)$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$a (a + b) + b (a + b) - 2 a (a + b)$

Step 1.2.2

Apply the distributive property.

$a \cdot a + a b + b (a + b) - 2 a (a + b)$

Step 1.2.3

Apply the distributive property.

$a \cdot a + a b + b a + b \cdot b - 2 a (a + b)$

$a \cdot a + a b + b a + b \cdot b - 2 a (a + b)$

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 $a$ by $a$ .

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

Step 1.3.1.2

Multiply $b$ by $b$ .

$a^{2} + a b + b a + b^{2} - 2 a (a + b)$

$a^{2} + a b + b a + b^{2} - 2 a (a + b)$

Step 1.3.2

Add $a b$ and $b a$ .

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Step 1.3.2.1

Reorder $b$ and $a$ .

$a^{2} + a b + a b + b^{2} - 2 a (a + b)$

Step 1.3.2.2

Add $a b$ and $a b$ .

$a^{2} + 2 a b + b^{2} - 2 a (a + b)$

$a^{2} + 2 a b + b^{2} - 2 a (a + b)$

$a^{2} + 2 a b + b^{2} - 2 a (a + b)$

Step 1.4

Apply the distributive property.

$a^{2} + 2 a b + b^{2} - 2 a \cdot a - 2 a b$

Step 1.5

Multiply $a$ by $a$ by adding the exponents.

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Step 1.5.1

Move $a$ .

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

Step 1.5.2

Multiply $a$ by $a$ .

$a^{2} + 2 a b + b^{2} - 2 a^{2} - 2 a b$

$a^{2} + 2 a b + b^{2} - 2 a^{2} - 2 a b$

$a^{2} + 2 a b + b^{2} - 2 a^{2} - 2 a b$

Step 2

Simplify by adding terms.

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Step 2.1

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

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Step 2.1.1

Subtract $2 a b$ from $2 a b$ .

$a^{2} + b^{2} - 2 a^{2} + 0$

Step 2.1.2

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

$a^{2} + b^{2} - 2 a^{2}$

$a^{2} + b^{2} - 2 a^{2}$

Step 2.2

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

$- a^{2} + b^{2}$

$- a^{2} + b^{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$