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Ma and Pa Math

Ma and Pa Math. Expanding Polynomials And Common Factoring. Review. Expanding Polynomials. The product of two binomials can be found by multiplying EACH term in one binomial by EACH term in the other binomial Then, simplify (collect like terms).

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Ma and Pa Math

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  1. Ma and Pa Math

  2. Expanding Polynomials And Common Factoring Review

  3. Expanding Polynomials • The product of two binomials can be found by multiplying EACH term in one binomial by EACH term in the other binomial • Then, simplify (collect like terms)

  4. Angelina and Brad go to the movies, where they meet Courtney and David. B C D A

  5. If they were to all shake hands with the people they are just meeting… who would shake hands with who? B C D A

  6. A and C B and C A and D B and D B C D A

  7. Expanding polynomials works the same way! Example 1: Expand and simplify. a) b) In this case, the 3 ‘meets’ the x and the 3 ‘meets’ the 2. In this case, the 2y is multiplied by y and the 2y is multiplied by 1.

  8. c) d)

  9. e)

  10. Common Factoring • When factoring polynomial expressions, look at both the numerical coefficients and the variables to find the greatest common factor (G.C.F.) • Look for the greatest common numerical factor and the variable with the highest degree of the variable common to each term • To check that you have factored correctly, EXPAND your answer (because EXPANDING is the opposite of FACTORING!)

  11. Example 2: Factor. a) b) c)

  12. Exponent Laws

  13. Radicals!

  14. Radicals and Exponents • A radical is a root to any degree E.g. is a squared root, is a cubed root. • A repeated multiplication of equal factors (the same number) can b expressed as a power Example: 3 x 3 x 3 x 3 = 34 34is the power  3 is the base  4 is the exponent

  15. Radicals and Exponents 53 = “5 to the three” 64 = “six to the four” Hizzo = “H to the Izzo”

  16. Radicals and Exponents 63 = 6 x 6 x 6

  17. Radicals and Exponents 52 x 55 = (5 x 5) x (5 x 5 x 5 x 5 x 5) = 57

  18. Radicals and Exponents 68 65 = = = 63

  19. Radicals and Exponents = (72) x (72) x (72) = (7 x 7) x ( 7 x 7) x (7 x 7) = (7 x 7) x ( 7 x 7) x (7 x 7) = 76

  20. Radicals and Exponents = (3 x 2) x ( 3 x 2) x (3 x 2) x (3 x 2) = (3 x 3 x 3 x 3) x (2 x 2 x 2 x 2) = (34) x (24)

  21. Radicals and Exponents = x x = =

  22. The Power of Negative Numbers • There is a difference between –32 and (–3)2 • The exponent affects ONLY the number it touches So, –32= –(3 x 3), but (–3)2 = (–3) x (–3) = –9 = 9

  23. Homework p. 399 # 1 – 3, 5 – 11 (alternating!) Challenge Pg. 401 #16 – 18

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