Basic Math Examples

$(2 a - 1) (2 a^{2} + 5 a + 4)$

Step 1

Expand $(2 a - 1) (2 a^{2} + 5 a + 4)$ by multiplying each term in the first expression by each term in the second expression.

$2 a (2 a^{2}) + 2 a (5 a) + 2 a \cdot 4 - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2

Simplify 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.

$2 \cdot 2 a \cdot a^{2} + 2 a (5 a) + 2 a \cdot 4 - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2.1.2

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

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Step 2.1.2.1

Move $a^{2}$ .

$2 \cdot 2 (a^{2} a) + 2 a (5 a) + 2 a \cdot 4 - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

$2 \cdot 2 (a^{2} a^{1}) + 2 a (5 a) + 2 a \cdot 4 - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2.1.2.2.2

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

$2 \cdot 2 a^{2 + 1} + 2 a (5 a) + 2 a \cdot 4 - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2.1.2.3

Add $2$ and $1$ .

$2 \cdot 2 a^{3} + 2 a (5 a) + 2 a \cdot 4 - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2.1.3

Multiply $2$ by $2$ .

$4 a^{3} + 2 a (5 a) + 2 a \cdot 4 - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$4 a^{3} + 2 \cdot 5 a \cdot a + 2 a \cdot 4 - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2.1.5

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

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Step 2.1.5.1

Move $a$ .

$4 a^{3} + 2 \cdot 5 (a \cdot a) + 2 a \cdot 4 - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2.1.5.2

Multiply $a$ by $a$ .

$4 a^{3} + 2 \cdot 5 a^{2} + 2 a \cdot 4 - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2.1.6

Multiply $2$ by $5$ .

$4 a^{3} + 10 a^{2} + 2 a \cdot 4 - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2.1.7

Multiply $4$ by $2$ .

$4 a^{3} + 10 a^{2} + 8 a - 1 (2 a^{2}) - 1 (5 a) - 1 \cdot 4$

Step 2.1.8

Multiply $2$ by $- 1$ .

$4 a^{3} + 10 a^{2} + 8 a - 2 a^{2} - 1 (5 a) - 1 \cdot 4$

Step 2.1.9

Multiply $5$ by $- 1$ .

$4 a^{3} + 10 a^{2} + 8 a - 2 a^{2} - 5 a - 1 \cdot 4$

Step 2.1.10

Multiply $- 1$ by $4$ .

$4 a^{3} + 10 a^{2} + 8 a - 2 a^{2} - 5 a - 4$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $2 a^{2}$ from $10 a^{2}$ .

$4 a^{3} + 8 a^{2} + 8 a - 5 a - 4$

Step 2.2.2

Subtract $5 a$ from $8 a$ .

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