Trigonometry Examples

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

Step 1

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

$(2 a b + c) (2 a b + c)$

Step 2

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

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Step 2.1

Apply the distributive property.

$2 a b (2 a b + c) + c (2 a b + c)$

Step 2.2

Apply the distributive property.

$2 a b (2 a b) + 2 a b c + c (2 a b + c)$

Step 2.3

Apply the distributive property.

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

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 $a$ by adding the exponents.

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Step 3.1.1.1

Move $a$ .

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

Step 3.1.1.2

Multiply $a$ by $a$ .

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

Step 3.1.2

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

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Step 3.1.2.1

Move $b$ .

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

Step 3.1.2.2

Multiply $b$ by $b$ .

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

Step 3.1.3

Multiply $2$ by $2$ .

$4 a^{2} b^{2} + 2 a b c + c (2 a b) + c \cdot c$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$4 a^{2} b^{2} + 2 a b c + 2 c a b + c \cdot c$

Step 3.1.5

Multiply $c$ by $c$ .

$4 a^{2} b^{2} + 2 a b c + 2 c a b + c^{2}$

Step 3.2

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

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Step 3.2.1

Move $c$ .

$4 a^{2} b^{2} + 2 a b c + 2 a b c + c^{2}$

Step 3.2.2

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

$4 a^{2} b^{2} + 4 a b c + c^{2}$