Algebra Examples

$(7 - 2 a) (4 a^{2} + 4 a + 3)$

Step 1

Expand $(7 - 2 a) (4 a^{2} + 4 a + 3)$ by multiplying each term in the first expression by each term in the second expression.

$7 (4 a^{2}) + 7 (4 a) + 7 \cdot 3 - 2 a (4 a^{2}) - 2 a (4 a) - 2 a \cdot 3$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $4$ by $7$ .

$28 a^{2} + 7 (4 a) + 7 \cdot 3 - 2 a (4 a^{2}) - 2 a (4 a) - 2 a \cdot 3$

Step 2.1.2

Multiply $4$ by $7$ .

$28 a^{2} + 28 a + 7 \cdot 3 - 2 a (4 a^{2}) - 2 a (4 a) - 2 a \cdot 3$

Step 2.1.3

Multiply $7$ by $3$ .

$28 a^{2} + 28 a + 21 - 2 a (4 a^{2}) - 2 a (4 a) - 2 a \cdot 3$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$28 a^{2} + 28 a + 21 - 2 \cdot 4 a \cdot a^{2} - 2 a (4 a) - 2 a \cdot 3$

Step 2.1.5

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

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Step 2.1.5.1

Move $a^{2}$ .

$28 a^{2} + 28 a + 21 - 2 \cdot 4 (a^{2} a) - 2 a (4 a) - 2 a \cdot 3$

Step 2.1.5.2

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

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Step 2.1.5.2.1

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

$28 a^{2} + 28 a + 21 - 2 \cdot 4 (a^{2} a^{1}) - 2 a (4 a) - 2 a \cdot 3$

Step 2.1.5.2.2

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

$28 a^{2} + 28 a + 21 - 2 \cdot 4 a^{2 + 1} - 2 a (4 a) - 2 a \cdot 3$

Step 2.1.5.3

Add $2$ and $1$ .

$28 a^{2} + 28 a + 21 - 2 \cdot 4 a^{3} - 2 a (4 a) - 2 a \cdot 3$

Step 2.1.6

Multiply $- 2$ by $4$ .

$28 a^{2} + 28 a + 21 - 8 a^{3} - 2 a (4 a) - 2 a \cdot 3$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$28 a^{2} + 28 a + 21 - 8 a^{3} - 2 \cdot 4 a \cdot a - 2 a \cdot 3$

Step 2.1.8

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

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Step 2.1.8.1

Move $a$ .

$28 a^{2} + 28 a + 21 - 8 a^{3} - 2 \cdot 4 (a \cdot a) - 2 a \cdot 3$

Step 2.1.8.2

Multiply $a$ by $a$ .

$28 a^{2} + 28 a + 21 - 8 a^{3} - 2 \cdot 4 a^{2} - 2 a \cdot 3$

Step 2.1.9

Multiply $- 2$ by $4$ .

$28 a^{2} + 28 a + 21 - 8 a^{3} - 8 a^{2} - 2 a \cdot 3$

Step 2.1.10

Multiply $3$ by $- 2$ .

$28 a^{2} + 28 a + 21 - 8 a^{3} - 8 a^{2} - 6 a$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $8 a^{2}$ from $28 a^{2}$ .

$20 a^{2} + 28 a + 21 - 8 a^{3} - 6 a$

Step 2.2.2

Subtract $6 a$ from $28 a$ .

$20 a^{2} + 22 a + 21 - 8 a^{3}$

Step 2.2.3

Simplify the expression.

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Step 2.2.3.1

Move $21$ .

$20 a^{2} + 22 a - 8 a^{3} + 21$

Step 2.2.3.2

Move $22 a$ .

$20 a^{2} - 8 a^{3} + 22 a + 21$

Step 2.2.3.3

Reorder $20 a^{2}$ and $- 8 a^{3}$ .

$- 8 a^{3} + 20 a^{2} + 22 a + 21$