Basic Math Examples

$(2 b + c) (b - 2 c)$

Step 1

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

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Step 1.1

Apply the distributive property.

$2 b (b - 2 c) + c (b - 2 c)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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Step 2.1.1.1

Move $b$ .

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

Step 2.1.1.2

Multiply $b$ by $b$ .

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

Step 2.1.2

Rewrite using the commutative property of multiplication.

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

Step 2.1.3

Multiply $2$ by $- 2$ .

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

Step 2.1.4

Rewrite using the commutative property of multiplication.

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

Step 2.1.5

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

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Step 2.1.5.1

Move $c$ .

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

Step 2.1.5.2

Multiply $c$ by $c$ .

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

Step 2.2

Add $- 4 b c$ and $c b$ .

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Step 2.2.1

Reorder $c$ and $b$ .

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

Step 2.2.2

Add $- 4 b c$ and $b c$ .

$2 b^{2} - 3 b c - 2 c^{2}$