Finite Math Examples

$- 7 m^{2} + 8 n^{2} - 4 n - (8 m^{2} - 4 m + 7 n - 8 m^{2} + 4 n^{2})$

Step 1

Simplify and reorder the polynomial.

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Step 1.1

Combine the opposite terms in $- 7 m^{2} + 8 n^{2} - 4 n - (8 m^{2} - 4 m + 7 n - 8 m^{2} + 4 n^{2})$ .

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Step 1.1.1

Subtract $8 m^{2}$ from $8 m^{2}$ .

$- 7 m^{2} + 8 n^{2} - 4 n - (- 4 m + 7 n + 0 + 4 n^{2})$

Step 1.1.2

Add $- 4 m + 7 n$ and $0$ .

$- 7 m^{2} + 8 n^{2} - 4 n - (- 4 m + 7 n + 4 n^{2})$

Step 1.2

Simplify each term.

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Step 1.2.1

Apply the distributive property.

$- 7 m^{2} + 8 n^{2} - 4 n - (- 4 m) - (7 n) - (4 n^{2})$

Step 1.2.2

Simplify.

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Step 1.2.2.1

Multiply $- 4$ by $- 1$ .

$- 7 m^{2} + 8 n^{2} - 4 n + 4 m - (7 n) - (4 n^{2})$

Step 1.2.2.2

Multiply $7$ by $- 1$ .

$- 7 m^{2} + 8 n^{2} - 4 n + 4 m - 7 n - (4 n^{2})$

Step 1.2.2.3

Multiply $4$ by $- 1$ .

$- 7 m^{2} + 8 n^{2} - 4 n + 4 m - 7 n - 4 n^{2}$

Step 1.3

Simplify by adding terms.

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Step 1.3.1

Subtract $4 n^{2}$ from $8 n^{2}$ .

$- 7 m^{2} + 4 n^{2} - 4 n + 4 m - 7 n$

Step 1.3.2

Subtract $7 n$ from $- 4 n$ .

$- 7 m^{2} + 4 n^{2} + 4 m - 11 n$

Step 2

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

$- 7 m^{2} \to 2$

$4 n^{2} \to 2$

$4 m \to 1$

$- 11 n \to 1$

Step 3

The largest exponent is the degree of the polynomial.

$2$