Multiply a polynomial by a monomial

key notes:

1. Definition:
   • A polynomial is an expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
   • A monomial is a polynomial with only one term.
2. Multiplying a Monomial by a Polynomial:
   • To multiply a monomial by a polynomial, distribute each term of the monomial to every term in the polynomial.
   • Example: 3�⋅(2�2+5�−1)3x⋅(2x2+5x−1)
     • Distribute 3x to each term: 3�⋅2�2+3�⋅5�−3�⋅13x⋅2x2+3x⋅5x−3x⋅1
3. Multiplication Rules:
   • Multiply coefficients together.
   • Add exponents when the base (variable) is the same.
     • Example: 2�3⋅4�2=8�3+2=8�52x3⋅4x2=8x3+2=8x5
4. Combining Like Terms:
   • After multiplying, combine like terms by adding or subtracting coefficients.
     • Example: 3�⋅2�2+3�⋅5�−3�⋅13x⋅2x2+3x⋅5x−3x⋅1
       • Combine like terms: 6�3+15�2−3�6x3+15x2−3x
5. Be Mindful of Signs:
   • Pay attention to the signs when distributing the monomial.
   • Example: (−2�)⋅(3�2−4�+1)(−2y)⋅(3y2−4y+1)
     • Distribute −2�−2y: −2�⋅3�2+(−2�)⋅(−4�)+(−2�)⋅1−2y⋅3y2+(−2y)⋅(−4y)+(−2y)⋅1
6. Practice with Examples:
   • Practice various examples to reinforce the concept.
   • Example: 4�⋅(2�2−3�+1)4a⋅(2a2−3a+1)
7. Real-Life Applications:
   • Understanding how to multiply polynomials by monomials is useful in algebraic expressions and equations, which are common in various real-life scenarios.
8. Check Your Answers:
   • Always check your final answer by simplifying and ensuring it makes sense in the context of the problem.
9. Review Properties of Exponents:
   • Knowledge of exponent rules is essential for simplifying expressions when dealing with monomials and polynomials.
10. Challenge Problems:
    • Challenge yourself with more complex problems to deepen your understanding.

Learn with an example

let’s practice!🖊️