Basic Math Examples

$| 5 a - 1 | | 7 a + 8 |$

Step 1

To multiply absolute values, multiply the terms inside each absolute value.

$| (5 a - 1) (7 a + 8) |$

Step 2

Expand $(5 a - 1) (7 a + 8)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$| 5 a (7 a + 8) - 1 (7 a + 8) |$

Step 2.2

Apply the distributive property.

$| 5 a (7 a) + 5 a \cdot 8 - 1 (7 a + 8) |$

Step 2.3

Apply the distributive property.

$| 5 a (7 a) + 5 a \cdot 8 - 1 (7 a) - 1 \cdot 8 |$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

$| 5 \cdot 7 a \cdot a + 5 a \cdot 8 - 1 (7 a) - 1 \cdot 8 |$

Step 3.1.2

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

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Step 3.1.2.1

Move $a$ .

$| 5 \cdot 7 (a \cdot a) + 5 a \cdot 8 - 1 (7 a) - 1 \cdot 8 |$

Step 3.1.2.2

Multiply $a$ by $a$ .

$| 5 \cdot 7 a^{2} + 5 a \cdot 8 - 1 (7 a) - 1 \cdot 8 |$

Step 3.1.3

Multiply $5$ by $7$ .

$| 35 a^{2} + 5 a \cdot 8 - 1 (7 a) - 1 \cdot 8 |$

Step 3.1.4

Multiply $8$ by $5$ .

$| 35 a^{2} + 40 a - 1 (7 a) - 1 \cdot 8 |$

Step 3.1.5

Multiply $7$ by $- 1$ .

$| 35 a^{2} + 40 a - 7 a - 1 \cdot 8 |$

Step 3.1.6

Multiply $- 1$ by $8$ .

$| 35 a^{2} + 40 a - 7 a - 8 |$

Step 3.2

Subtract $7 a$ from $40 a$ .

$| 35 a^{2} + 33 a - 8 |$