Algebra Examples

$(4 b - 8 c) (\frac{b}{2} - \frac{c}{4})$

Step 1

Expand $(4 b - 8 c) (\frac{b}{2} - \frac{c}{4})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 b (\frac{b}{2} - \frac{c}{4}) - 8 c (\frac{b}{2} - \frac{c}{4})$

Step 1.2

Apply the distributive property.

$4 b \frac{b}{2} + 4 b (- \frac{c}{4}) - 8 c (\frac{b}{2} - \frac{c}{4})$

Step 1.3

Apply the distributive property.

$4 b \frac{b}{2} + 4 b (- \frac{c}{4}) - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

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

Cancel the common factor of $2$ .

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Step 2.1.1.1

Factor $2$ out of $4 b$ .

$2 (2 b) \frac{b}{2} + 4 b (- \frac{c}{4}) - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.1.2

Cancel the common factor.

$2 (2 b) \frac{b}{2} + 4 b (- \frac{c}{4}) - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.1.3

Rewrite the expression.

$2 b \cdot b + 4 b (- \frac{c}{4}) - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.2

Raise $b$ to the power of $1$ .

$2 (b^{1} b) + 4 b (- \frac{c}{4}) - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.3

Raise $b$ to the power of $1$ .

$2 (b^{1} b^{1}) + 4 b (- \frac{c}{4}) - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 b^{1 + 1} + 4 b (- \frac{c}{4}) - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.5

Add $1$ and $1$ .

$2 b^{2} + 4 b (- \frac{c}{4}) - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.6

Cancel the common factor of $4$ .

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Step 2.1.6.1

Move the leading negative in $- \frac{c}{4}$ into the numerator.

$2 b^{2} + 4 b \frac{- c}{4} - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.6.2

Factor $4$ out of $4 b$ .

$2 b^{2} + 4 (b) \frac{- c}{4} - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.6.3

Cancel the common factor.

$2 b^{2} + 4 b \frac{- c}{4} - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.6.4

Rewrite the expression.

$2 b^{2} + b (- c) - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$2 b^{2} - b c - 8 c \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.8

Cancel the common factor of $2$ .

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Step 2.1.8.1

Factor $2$ out of $- 8 c$ .

$2 b^{2} - b c + 2 (- 4 c) \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.8.2

Cancel the common factor.

$2 b^{2} - b c + 2 (- 4 c) \frac{b}{2} - 8 c (- \frac{c}{4})$

Step 2.1.8.3

Rewrite the expression.

$2 b^{2} - b c - 4 c b - 8 c (- \frac{c}{4})$

Step 2.1.9

Cancel the common factor of $4$ .

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Step 2.1.9.1

Move the leading negative in $- \frac{c}{4}$ into the numerator.

$2 b^{2} - b c - 4 c b - 8 c \frac{- c}{4}$

Step 2.1.9.2

Factor $4$ out of $- 8 c$ .

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

Step 2.1.9.3

Cancel the common factor.

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

Step 2.1.9.4

Rewrite the expression.

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

Step 2.1.10

Multiply $- 1$ by $- 2$ .

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

Step 2.1.11

Raise $c$ to the power of $1$ .

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

Step 2.1.12

Raise $c$ to the power of $1$ .

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

Step 2.1.13

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 2.1.14

Add $1$ and $1$ .

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

Step 2.2

Subtract $4 c b$ from $- b c$ .

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Step 2.2.1

Move $c$ .

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

Step 2.2.2

Subtract $4 b c$ from $- b c$ .

$2 b^{2} - 5 b c + 2 c^{2}$