Trigonometry Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $a$ by $a$ .

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

Step 3.1.2

Multiply $b$ by $b$ .

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

Step 3.2

Add $a b$ and $b a$ .

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Step 3.2.1

Reorder $b$ and $a$ .

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

Step 3.2.2

Add $a b$ and $a b$ .

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

Step 4

Since the two sides have been shown to be equivalent, the equation is an identity.

${(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ is an identity.