Lesson about Multiplying Polynomials.pptx

This powerpoint is a lesson on Multiplying Polynomials. In this material it is shown here the different cases of multiplying polynomials that will surely be useful by anyone.

1. LESSON 3.5: MULTIPLYING POLYNOMIALS

2. LESSON 3.5: MULTIPLYING POLYNOMIALS WARM UP ACTIVITY: I. Simplify 1. 2. 3. 4. 5.  

3. LESSON 3.5: MULTIPLYING POLYNOMIALS

4. Monomial – an algebraic expression consisting of one term but can have multiple variables and a higher degree . degree coefficient variable/s   A. MONOMIAL BY A MONOMIAL In monomial, the each term consist of only multiplication and exponential operations. There are no addition, subtraction, or division operations within a single monomial. LESSON 3.5: MULTIPLYING POLYNOMIALS

5. To multiply two or more monomials , multiply the numerical coefficients and apply the laws of exponents for product . Examples: 1. Solution:   A. MONOMIAL BY A MONOMIAL PRODUCT OF POWERS POWER OF A POWER POWER OF A PRODUCT   LESSON 3.5: MULTIPLYING POLYNOMIALS

6. Examples: Solution:   A. MONOMIAL BY A MONOMIAL 3.   Solution: )       LESSON 3.5: MULTIPLYING POLYNOMIALS

7. Examples: 4. 5 . Solution: Solution:   A. MONOMIAL BY A MONOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

8. Examples: Let’s Try: 6. 7. Solution: 8. 9. ( 10. )   A. MONOMIAL BY A MONOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

9. Polynomial – an algebraic expression of two or more terms composed of coefficients , variables , exponents , constants , and operations (except for division by variables/contain variables in the denominator ). operations exponent variables constant coefficients   B. MONOMIAL BY A POLYNOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

10. To multiply a monomial by a polynomial , use the distributive property of multiplication over addition observing the law of exponents for product . Examples: Solution:   B. MONOMIAL BY A POLYNOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

11. E xamples: 2. Solution:   B. MONOMIAL BY A POLYNOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

12. E xamples: 3. Solution: ]   B. MONOMIAL BY A POLYNOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

13. E xamples: 3. Solution:   B. MONOMIAL BY A POLYNOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

14. Let’s Try 4. 5. 6. 7. 8.   B. MONOMIAL BY A POLYNOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

15. Binomial – a type of polynomial that consists exactly two terms . exponent constant coefficients variable operation (+/-)   C. BINOMIAL BY A BINOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

16. To multiply binomial, simply distribute the 1 st term of the 1 st binomial to each term of the other binomial then distribute the second term to each term of the other binomial and simplify the results by combining similar terms. (FOIL METHOD) C. BINOMIAL BY A BINOMIAL 20 x 46 _______ 120 80 _______ 920 Another way is the VERTICAL METHOD of multiplying. It’s same as multiplying integers. LESSON 3.5: MULTIPLYING POLYNOMIALS

17. Examples: 1. FOIL METHOD: F 0 I L 4x + 2 combine similar terms   C. BINOMIAL BY A BINOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

18. Examples: 1. Vertical Method : __________________ _______________________   C. BINOMIAL BY A BINOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

19. Examples: 1. FOIL METHOD: F 0 I L )( )+ (2)(-1)( )+(3)(4)( )+(3)(-1) )]+ [(2)(-1)( )]+[(3)(4)( )]+[(3)(-1)] )( + (-2)( )+(12)( )+(-3) -3 combine similar terms   C. BINOMIAL BY A BINOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

20. Examples: 2. Vertical Method : __________________ _______________________   C. BINOMIAL BY A BINOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

21. Let’s Try! 1. 2.   C. BINOMIAL BY A BINOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

22. TRINOMIAL - a type of polynomial with exactly three terms . exponent operations (add & sub) constant coefficients variable(s)   D. BINOMIAL BY A TRINOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

23. To multiply a binomial with more than one term by a polynomial with three or more terms, simply distribute the first term of the first polynomial to each term of the other polynomial . Repeat the procedure up to the last term and simplify the results by combining similar terms. D. BINOMIAL BY A TRINOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

24. Examples: Find the product Using Distributive Property:   D. BINOMIAL BY A TRINOMIAL combine similar terms =6x 2 +8xy +5 +20y +2x +15x =6x 2 +8xy +5 +20y +17x LESSON 3.5: MULTIPLYING POLYNOMIALS

25. Examples: Find the product Using Vertical Method: _____________________   D. BINOMIAL BY A TRINOMIAL combine similar terms 15x +20y +5 6x 2 +8xy +2x 6x 2 +8xy +17x +5 +20y 15x +2x LESSON 3.5: MULTIPLYING POLYNOMIALS

26. Examples: Find the product 2. Using Distributive Property:   D. BINOMIAL BY A TRINOMIAL = 9x 2 -12xy +15xz -8y +6x +10z LESSON 3.5: MULTIPLYING POLYNOMIALS

27. Examples: Find the product Using Vertical Method: _____________________   D. BINOMIAL BY A TRINOMIAL 6x +8y +10z 9x 2 -12xy +15xz 9x 2 +15xz +6x +10z +8y Although, and are aligned and are also aligned, we cannot combine them because they are not similar.   -12xy LESSON 3.5: MULTIPLYING POLYNOMIALS

28. Examples: Find the product 3. Using Distributive Property: combine similar terms   D. BINOMIAL BY A TRINOMIAL = 6x 2 + xy -4xz -35   -10yz LESSON 3.5: MULTIPLYING POLYNOMIALS

29. Examples: Find the product 3. Using Vertical Method: ___________________ -------- ---------------- ____________________________   D. BINOMIAL BY A TRINOMIAL Although, and are aligned, we cannot combine them because they are not similar.   6x 2 + xy -4xz -10yz +35   LESSON 3.5: MULTIPLYING POLYNOMIALS

30. LET’S TRY THIS OUT! )   D. BINOMIAL BY A TRINOMIAL LESSON 3.5: MULTIPLYING POLYNOMIALS

31. A. Instruction: Find the product of the following expressions using Distributive Method 1. 3m 2 n 3 (4mn 4 ) 2. 5xy 3. 7k (3k 3 - 2k 2 +7) B. Instruction: Find the product of the following expressions using FOIL Method 4. (2x+3)(3x+1) 5. (2x 2 – 3y 4 )(3x 3 +y 2 ) C. Instruction: Find the product of the following expressions using Vertical Method 6. (3x+9y)(2x+5y – 4z) 7. (3x+9y)(2x 2 -5y 2 – 4z 2 )   Assignment 3.6 LESSON 3.5: MULTIPLYING POLYNOMIALS

32. THANK YOU!