Basic Math Examples

$(a^{2} - 2 a) (2 a - 4)$

Step 1

Expand $(a^{2} - 2 a) (2 a - 4)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$a^{2} (2 a - 4) - 2 a (2 a - 4)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $a$ .

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

Step 2.1.2.2

Multiply $a$ by $a^{2}$ .

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Step 2.1.2.2.1

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

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

Step 2.1.2.2.2

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

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

Step 2.1.2.3

Add $1$ and $2$ .

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

Step 2.1.3

Move $- 4$ to the left of $a^{2}$ .

$2 a^{3} - 4 \cdot a^{2} - 2 a (2 a) - 2 a \cdot - 4$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$2 a^{3} - 4 a^{2} - 2 \cdot 2 a \cdot a - 2 a \cdot - 4$

Step 2.1.5

Multiply $a$ by $a$ by adding the exponents.

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Step 2.1.5.1

Move $a$ .

$2 a^{3} - 4 a^{2} - 2 \cdot 2 (a \cdot a) - 2 a \cdot - 4$

Step 2.1.5.2

Multiply $a$ by $a$ .

$2 a^{3} - 4 a^{2} - 2 \cdot 2 a^{2} - 2 a \cdot - 4$

Step 2.1.6

Multiply $- 2$ by $2$ .

$2 a^{3} - 4 a^{2} - 4 a^{2} - 2 a \cdot - 4$

Step 2.1.7

Multiply $- 4$ by $- 2$ .

$2 a^{3} - 4 a^{2} - 4 a^{2} + 8 a$

Step 2.2

Subtract $4 a^{2}$ from $- 4 a^{2}$ .

$2 a^{3} - 8 a^{2} + 8 a$