Finite Math Examples

$(2 x - 9) (5 x + 2)$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Expand $(2 x - 9) (5 x + 2)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$2 x (5 x + 2) - 9 (5 x + 2)$

Step 1.1.2

Apply the distributive property.

$2 x (5 x) + 2 x \cdot 2 - 9 (5 x + 2)$

Step 1.1.3

Apply the distributive property.

$2 x (5 x) + 2 x \cdot 2 - 9 (5 x) - 9 \cdot 2$

Step 1.2

Simplify and combine like terms.

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Step 1.2.1

Simplify each term.

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Step 1.2.1.1

Rewrite using the commutative property of multiplication.

$2 \cdot 5 x \cdot x + 2 x \cdot 2 - 9 (5 x) - 9 \cdot 2$

Step 1.2.1.2

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

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Step 1.2.1.2.1

Move $x$ .

$2 \cdot 5 (x \cdot x) + 2 x \cdot 2 - 9 (5 x) - 9 \cdot 2$

Step 1.2.1.2.2

Multiply $x$ by $x$ .

$2 \cdot 5 x^{2} + 2 x \cdot 2 - 9 (5 x) - 9 \cdot 2$

Step 1.2.1.3

Multiply $2$ by $5$ .

$10 x^{2} + 2 x \cdot 2 - 9 (5 x) - 9 \cdot 2$

Step 1.2.1.4

Multiply $2$ by $2$ .

$10 x^{2} + 4 x - 9 (5 x) - 9 \cdot 2$

Step 1.2.1.5

Multiply $5$ by $- 9$ .

$10 x^{2} + 4 x - 45 x - 9 \cdot 2$

Step 1.2.1.6

Multiply $- 9$ by $2$ .

$10 x^{2} + 4 x - 45 x - 18$

Step 1.2.2

Subtract $45 x$ from $4 x$ .

$10 x^{2} - 41 x - 18$

Step 2

The largest exponent is the degree of the polynomial.

$2$