Finite Math Examples

$(6 x - 5) (8 x^{2} + 4 x - 7)$

Step 1

Expand $(6 x - 5) (8 x^{2} + 4 x - 7)$ by multiplying each term in the first expression by each term in the second expression.

$6 x (8 x^{2}) + 6 x (4 x) + 6 x \cdot - 7 - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

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.

$6 \cdot 8 x \cdot x^{2} + 6 x (4 x) + 6 x \cdot - 7 - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

Step 2.1.2

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

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Step 2.1.2.1

Move $x^{2}$ .

$6 \cdot 8 (x^{2} x) + 6 x (4 x) + 6 x \cdot - 7 - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

$6 \cdot 8 (x^{2} x^{1}) + 6 x (4 x) + 6 x \cdot - 7 - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

Step 2.1.2.2.2

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

$6 \cdot 8 x^{2 + 1} + 6 x (4 x) + 6 x \cdot - 7 - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

Step 2.1.2.3

Add $2$ and $1$ .

$6 \cdot 8 x^{3} + 6 x (4 x) + 6 x \cdot - 7 - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

Step 2.1.3

Multiply $6$ by $8$ .

$48 x^{3} + 6 x (4 x) + 6 x \cdot - 7 - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$48 x^{3} + 6 \cdot 4 x \cdot x + 6 x \cdot - 7 - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

Step 2.1.5

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1.5.1

Move $x$ .

$48 x^{3} + 6 \cdot 4 (x \cdot x) + 6 x \cdot - 7 - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

Step 2.1.5.2

Multiply $x$ by $x$ .

$48 x^{3} + 6 \cdot 4 x^{2} + 6 x \cdot - 7 - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

Step 2.1.6

Multiply $6$ by $4$ .

$48 x^{3} + 24 x^{2} + 6 x \cdot - 7 - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

Step 2.1.7

Multiply $- 7$ by $6$ .

$48 x^{3} + 24 x^{2} - 42 x - 5 (8 x^{2}) - 5 (4 x) - 5 \cdot - 7$

Step 2.1.8

Multiply $8$ by $- 5$ .

$48 x^{3} + 24 x^{2} - 42 x - 40 x^{2} - 5 (4 x) - 5 \cdot - 7$

Step 2.1.9

Multiply $4$ by $- 5$ .

$48 x^{3} + 24 x^{2} - 42 x - 40 x^{2} - 20 x - 5 \cdot - 7$

Step 2.1.10

Multiply $- 5$ by $- 7$ .

$48 x^{3} + 24 x^{2} - 42 x - 40 x^{2} - 20 x + 35$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Subtract $40 x^{2}$ from $24 x^{2}$ .

$48 x^{3} - 16 x^{2} - 42 x - 20 x + 35$

Step 2.2.2

Subtract $20 x$ from $- 42 x$ .

$48 x^{3} - 16 x^{2} - 62 x + 35$