Algebra Examples

$2 {(a b + c)}^{2} + 3 c (a b + c) - 1$

Step 1

Simplify each term.

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Step 1.1

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

$2 ((a b + c) (a b + c)) + 3 c (a b + c) - 1$

Step 1.2

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

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Step 1.2.1

Apply the distributive property.

$2 (a b (a b + c) + c (a b + c)) + 3 c (a b + c) - 1$

Step 1.2.2

Apply the distributive property.

$2 (a b (a b) + a b c + c (a b + c)) + 3 c (a b + c) - 1$

Step 1.2.3

Apply the distributive property.

$2 (a b (a b) + a b c + c (a b) + c \cdot c) + 3 c (a b + c) - 1$

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 $a$ by adding the exponents.

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Step 1.3.1.1.1

Move $a$ .

$2 (a \cdot a b \cdot b + a b c + c (a b) + c \cdot c) + 3 c (a b + c) - 1$

Step 1.3.1.1.2

Multiply $a$ by $a$ .

$2 (a^{2} b \cdot b + a b c + c (a b) + c \cdot c) + 3 c (a b + c) - 1$

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $b$ .

$2 (a^{2} (b \cdot b) + a b c + c (a b) + c \cdot c) + 3 c (a b + c) - 1$

Step 1.3.1.2.2

Multiply $b$ by $b$ .

$2 (a^{2} b^{2} + a b c + c (a b) + c \cdot c) + 3 c (a b + c) - 1$

Step 1.3.1.3

Multiply $c$ by $c$ .

$2 (a^{2} b^{2} + a b c + c a b + c^{2}) + 3 c (a b + c) - 1$

Step 1.3.2

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

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Step 1.3.2.1

Move $c$ .

$2 (a^{2} b^{2} + a b c + a b c + c^{2}) + 3 c (a b + c) - 1$

Step 1.3.2.2

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

$2 (a^{2} b^{2} + 2 a b c + c^{2}) + 3 c (a b + c) - 1$

Step 1.4

Apply the distributive property.

$2 (a^{2} b^{2}) + 2 (2 a b c) + 2 c^{2} + 3 c (a b + c) - 1$

Step 1.5

Multiply $2$ by $2$ .

$2 a^{2} b^{2} + 4 (a b c) + 2 c^{2} + 3 c (a b + c) - 1$

Step 1.6

Remove parentheses.

$2 a^{2} b^{2} + 4 a b c + 2 c^{2} + 3 c (a b + c) - 1$

Step 1.7

Apply the distributive property.

$2 a^{2} b^{2} + 4 a b c + 2 c^{2} + 3 c (a b) + 3 c \cdot c - 1$

Step 1.8

Multiply $c$ by $c$ by adding the exponents.

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Step 1.8.1

Move $c$ .

$2 a^{2} b^{2} + 4 a b c + 2 c^{2} + 3 c a b + 3 (c \cdot c) - 1$

Step 1.8.2

Multiply $c$ by $c$ .

$2 a^{2} b^{2} + 4 a b c + 2 c^{2} + 3 c a b + 3 c^{2} - 1$

Step 2

Add $4 a b c$ and $3 c a b$ .

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Step 2.1

Move $c$ .

$2 a^{2} b^{2} + 2 c^{2} + 4 a b c + 3 a b c + 3 c^{2} - 1$

Step 2.2

Add $4 a b c$ and $3 a b c$ .

$2 a^{2} b^{2} + 2 c^{2} + 7 a b c + 3 c^{2} - 1$

Step 3

Add $2 c^{2}$ and $3 c^{2}$ .

$2 a^{2} b^{2} + 5 c^{2} + 7 a b c - 1$

Step 4

Move $5 c^{2}$ .

$2 a^{2} b^{2} + 7 a b c + 5 c^{2} - 1$