Finite Math Examples

$(6 x - 5) (3 - x)$

Step 1

Expand $(6 x - 5) (3 - x)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$6 x (3 - x) - 5 (3 - x)$

Step 1.2

Apply the distributive property.

$6 x \cdot 3 + 6 x (- x) - 5 (3 - x)$

Step 1.3

Apply the distributive property.

$6 x \cdot 3 + 6 x (- x) - 5 \cdot 3 - 5 (- x)$

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

Multiply $3$ by $6$ .

$18 x + 6 x (- x) - 5 \cdot 3 - 5 (- x)$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$18 x + 6 \cdot - 1 x \cdot x - 5 \cdot 3 - 5 (- x)$

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

$18 x + 6 \cdot - 1 (x \cdot x) - 5 \cdot 3 - 5 (- x)$

Step 2.1.3.2

Multiply $x$ by $x$ .

$18 x + 6 \cdot - 1 x^{2} - 5 \cdot 3 - 5 (- x)$

Step 2.1.4

Multiply $6$ by $- 1$ .

$18 x - 6 x^{2} - 5 \cdot 3 - 5 (- x)$

Step 2.1.5

Multiply $- 5$ by $3$ .

$18 x - 6 x^{2} - 15 - 5 (- x)$

Step 2.1.6

Multiply $- 1$ by $- 5$ .

$18 x - 6 x^{2} - 15 + 5 x$

Step 2.2

Add $18 x$ and $5 x$ .

$23 x - 6 x^{2} - 15$

Step 3

Reorder $23 x$ and $- 6 x^{2}$ .

$- 6 x^{2} + 23 x - 15$