Finite Math Examples

$f (x) = (x^{6} + 7) (x^{10} + 9)$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Expand

$(x^{6} + 7) (x^{10} + 9)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$x^{6} (x^{10} + 9) + 7 (x^{10} + 9)$

Step 1.1.2

Apply the distributive property.

$x^{6} x^{10} + x^{6} \cdot 9 + 7 (x^{10} + 9)$

Step 1.1.3

Apply the distributive property.

$x^{6} x^{10} + x^{6} \cdot 9 + 7 x^{10} + 7 \cdot 9$

Step 1.2

Simplify each term.

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Step 1.2.1

Multiply

$x^{6}$ by

$x^{10}$ by adding the exponents.

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Step 1.2.1.1

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{6 + 10} + x^{6} \cdot 9 + 7 x^{10} + 7 \cdot 9$

Step 1.2.1.2

Add

$6$ and

$10$ .

$x^{16} + x^{6} \cdot 9 + 7 x^{10} + 7 \cdot 9$

Step 1.2.2

Move

$9$ to the left of

$x^{6}$ .

$x^{16} + 9 \cdot x^{6} + 7 x^{10} + 7 \cdot 9$

Step 1.2.3

Multiply

$7$ by

$9$ .

$x^{16} + 9 x^{6} + 7 x^{10} + 63$

Step 2

The largest exponent is the degree of the polynomial.

$16$