Perform the indicated operations. m(5m-2) + 9(5-m)

Verified step by step guidance

1. Identify the expression to simplify: \(m(5m - 2) + 9(5 - m)\).
2. Apply the distributive property to each term: multiply \(m\) by each term inside the first parentheses and \(9\) by each term inside the second parentheses. This gives \(m \times 5m\), \(m \times (-2)\), \(9 \times 5\), and \(9 \times (-m)\).
3. Write out the distributed terms explicitly: \$5m^2 - 2m + 45 - 9m$.
4. Combine like terms by grouping the terms with \(m\) together: \(-2m - 9m\).
5. Simplify the expression by adding the like terms and write the final simplified expression as \$5m^2 - 11m + 45$.

Key Concepts

Distributive Property

The distributive property allows you to multiply a single term by each term inside a parenthesis. For example, a(b + c) = ab + ac. This property is essential for expanding expressions like m(5m - 2) and 9(5 - m) before combining like terms.

Combining Like Terms

Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. After expanding expressions, you group terms such as 5m² and -9m to simplify the expression into a more manageable form.

Polynomial Addition

Polynomial addition is the process of adding two or more polynomial expressions by combining like terms. Understanding how to add polynomials helps in correctly performing the indicated operations and simplifying the final expression.