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Mastering Polynomial Multiplication

Learn how to apply the distributive property to multiply polynomials efficiently. Understand the rules for adding, subtracting, multiplying, and dividing terms. Practice multiplying complex polynomials and binomials. Engage in various exercises to enhance your skills in polynomial multiplication.

richarddaniel
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Mastering Polynomial Multiplication

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  1. Aim: How do we multiply polynomials? Do Now: • Simplify (5g2 + 3g – 1) – (2g2 – 3g + 2) 2) Simplify Homework #17-

  2. Homework Review

  3. What is the distributive property?How do we use it? Example: 2(3x + 5)

  4. The distributive property… *…says that when a number is multiplied by the sum/difference of two or more numbers, the first number can be distributed to each number and multiplied by each of them separately. Example:2(3x + 5) 2 will be multiplied by 3x 2 will be multiplied by 5 In simpler terms…

  5. Some things to remember: • The exponents of a term ONLY change when you are or . • The exponents of a term STAY THE SAME when you are or . • When you multiply terms with the same base, you the exponents.

  6. In other words: WHEN ADDING/SUBTRACTING: • To subtract, keep – change – change! • Find like terms. • Add coefficients. • Exponents stay the SAME. WHEN MULTIPLYING/DIVIDING: • Multiply/Divide the coefficients. • Multiply/Divide the variables by adding/subtracting the exponents. • Exponents may CHANGE.

  7. Let’s apply the distributive property to more complex polynomials 2x(3x + 5) -2x²(3x² - 4x +1)

  8. You try! Ex: -5x²(x² - 2x + 4)

  9. *Important to remember… • Distribute • Multiply coefficients • Add exponents • Simplify

  10. You try! 1) What is the product of 2r² - 5 and 3r 2) What is the product of -3x²y²(2xy² - 3y²) 3) What is the product of 2a²(4a³ +3a² + 2) 4) *Challenge: What is the product of (4x2– 12x + 6)

  11. Multiplying Binomials (2x + 3) (x + 2)

  12. To Multiply Binomials (product): Multiply the first number in the first binomial by EVERYTHING in the second binomial. Multiply the second number in the first binomial by EVERYTHING in the second binomial. Be careful with the SIGNS!! Then, combine like terms.

  13. Method 2: Box Method (2x + 3)(x + 2) 2x +3 x +2

  14. Example (-2x + 1)(x - 3)

  15. You Try! • (4x + 2)(2x + 3) • (x – 3)(x + 4) • (-2x + 3)(x – 3) Challenge: 4. (2x2 + 4)(-2x + 3)

  16. Practice Time! Worksheet do odd problems

  17. Index Card Activity 1) Meet with a partner • If you are a monomial, you need to pair up with a polynomial • If you are a polynomial, you need to pair up with a monomial 2) On a separate sheet of paper multiply by each other using the distributive property 3) Hand in your index card and be sure to show all work!

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