Algebra Examples

$(3 - c^{2} d) (4 - 4 c^{2} d)$

Step 1

Expand $(3 - c^{2} d) (4 - 4 c^{2} d)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 (4 - 4 c^{2} d) - c^{2} d (4 - 4 c^{2} d)$

Step 1.2

Apply the distributive property.

$3 \cdot 4 + 3 (- 4 c^{2} d) - c^{2} d (4 - 4 c^{2} d)$

Step 1.3

Apply the distributive property.

$3 \cdot 4 + 3 (- 4 c^{2} d) - c^{2} d \cdot 4 - c^{2} d (- 4 c^{2} d)$

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 $3$ by $4$ .

$12 + 3 (- 4 c^{2} d) - c^{2} d \cdot 4 - c^{2} d (- 4 c^{2} d)$

Step 2.1.2

Multiply $- 4$ by $3$ .

$12 - 12 (c^{2} d) - c^{2} d \cdot 4 - c^{2} d (- 4 c^{2} d)$

Step 2.1.3

Multiply $4$ by $- 1$ .

$12 - 12 c^{2} d - 4 c^{2} d - c^{2} d (- 4 c^{2} d)$

Step 2.1.4

Multiply $c^{2}$ by $c^{2}$ by adding the exponents.

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Step 2.1.4.1

Move $c^{2}$ .

$12 - 12 c^{2} d - 4 c^{2} d - (c^{2} c^{2}) d (- 4 d)$

Step 2.1.4.2

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

$12 - 12 c^{2} d - 4 c^{2} d - c^{2 + 2} d (- 4 d)$

Step 2.1.4.3

Add $2$ and $2$ .

$12 - 12 c^{2} d - 4 c^{2} d - c^{4} d (- 4 d)$

Step 2.1.5

Multiply $d$ by $d$ by adding the exponents.

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Step 2.1.5.1

Move $d$ .

$12 - 12 c^{2} d - 4 c^{2} d - c^{4} (d \cdot d) \cdot - 4$

Step 2.1.5.2

Multiply $d$ by $d$ .

$12 - 12 c^{2} d - 4 c^{2} d - c^{4} d^{2} \cdot - 4$

Step 2.1.6

Multiply $- 4$ by $- 1$ .

$12 - 12 c^{2} d - 4 c^{2} d + 4 c^{4} d^{2}$

Step 2.2

Subtract $4 c^{2} d$ from $- 12 c^{2} d$ .

$12 - 16 c^{2} d + 4 c^{4} d^{2}$

Step 3

Move $12$ .

$- 16 c^{2} d + 4 c^{4} d^{2} + 12$

Step 4

Reorder $- 16 c^{2} d$ and $4 c^{4} d^{2}$ .

$4 c^{4} d^{2} - 16 c^{2} d + 12$