Finite Math Examples

$5 (x^{2} + 3 y) - y (x^{2} + 5 y)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$5 x^{2} + 5 (3 y) - y (x^{2} + 5 y)$

Step 1.2

Multiply $3$ by $5$ .

$5 x^{2} + 15 y - y (x^{2} + 5 y)$

Step 1.3

Apply the distributive property.

$5 x^{2} + 15 y - y x^{2} - y (5 y)$

Step 1.4

Rewrite using the commutative property of multiplication.

$5 x^{2} + 15 y - y x^{2} - 1 \cdot 5 y \cdot y$

Step 1.5

Simplify each term.

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Step 1.5.1

Multiply $y$ by $y$ by adding the exponents.

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Step 1.5.1.1

Move $y$ .

$5 x^{2} + 15 y - y x^{2} - 1 \cdot 5 (y \cdot y)$

Step 1.5.1.2

Multiply $y$ by $y$ .

$5 x^{2} + 15 y - y x^{2} - 1 \cdot 5 y^{2}$

Step 1.5.2

Multiply $- 1$ by $5$ .

$5 x^{2} + 15 y - y x^{2} - 5 y^{2}$

Step 2

Identify the exponents on the variables in each term, and add them together to find the degree of each term.

$5 x^{2} \to 2$

$15 y \to 1$

$- y x^{2} \to 3$

$- 5 y^{2} \to 2$

Step 3

The largest exponent is the degree of the polynomial.

$3$