Basic Math Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Apply the distributive property.

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

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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 $a$ .

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

Step 3.1.1.2

Multiply $a$ by $a$ .

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

Step 3.1.2

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

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Step 3.1.2.1

Move $c$ .

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

Step 3.1.2.2

Multiply $c$ by $c$ .

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

Step 3.1.3

Multiply $b$ by $b$ .

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

Step 3.2

Reorder $b$ and $a$ .

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

Step 3.3

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

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