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Multiplying Two Binomials

F. Multiplying Two Binomials. O. I. L. To EXPAND two binomials we use a version of the distributive law called FOIL. Step 1 : Multiply the F IRST terms in the brackets. F. Step 2 : Multiply the O UTSIDE terms. O. Step 3 : Multiply the I NSIDE terms. I.

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Multiplying Two Binomials

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  1. F Multiplying Two Binomials O I L

  2. To EXPAND two binomials we use a version of the distributive law called FOIL • Step 1: Multiply the FIRST terms in the brackets. F

  3. Step 2: Multiply the OUTSIDE terms. O

  4. Step 3: Multiply the INSIDE terms. I

  5. Step 4: Multiply the LAST terms. L

  6. Step 5: Collect like terms.

  7. Example FOIL

  8. More…

  9. Factoring Trinomials in the form x2 + bx + c

  10. Factoring Simple Trinomials x2 + 10 x + 16 = (x + 2)(x + 8) Check by FOILing = x2 + 8x + 2x + 16 = x2 + 10x + 16 x2 + 9x + 20 x2 + 11x + 24 = (x + 5)(x + 4) = (x + 8)(x + 3) What relationship is there between product form and factored form? x2 + 5x + 4 = (x + 4)(x + 1)

  11. Factoring Simple Trinomials Many trinomials can be written as the product of 2 binomials. Recall: (x + 4)(x + 3) = x2 + 3x + 4x + 12 = x2 + 7x + 12 The middle term of a simple trinomial is the SUMof the last two terms of the binomials. The last term of a simple trinomial is the PRODUCT of the last two terms of the binomials. Therefore this type of factoring is referred to as SUM-PRODUCT!

  12. To factor trinomials, you ask yourself… “What numbers multiply to the last term and add to the middle term?" x12 +7 x2 + 7x + 12 1,12 13 2,6 8 (x + 3)(x + 4) 3,4 7

  13. Factor: x2 – 8x +12 – 8 x 12 ( x – 2)( x – 6) 1, 12 13 -1, -12 -13 2, 6 8 -2, -6 -8

  14. Factor: m2 – 5m -14 x (-14) -5 13 -1, 14 (m + 2) (m – 7) -13 1, -14 5 -2, 7 -5 2, -7

  15. Factor: x2 - 11x + 24 x2 + 13x + 36 x2 - 14x + 33

  16. Factor: x2 + 12x + 32 x2 - 20x + 75 x2 + 4x – 45 x2 + 17x + 72 x2 - 7x – 8

  17. Factor: - 5t – 3t2 + 15 + 4t2 – 3 - 3t STEP 1: Combine Like terms t2 – 8t +12 ( x – 2)( x – 6) x 12 - 8 1, 12 13 -1, -12 -13 2, 6 8 -2, -6 -8

  18. Factor: 7q2 – 14q - 21 STEP 1: Pull out the GCF 7 ( q2 –2q –3) 7 ( q – 3)( q + 1) -2 -3 -1, 3 2 -3, 1 -2

  19. To Summarize: • Always check to see if you can simplify first! • Then check to see if you can pull out a common factor. • Write 2 sets of brackets with x in the first position. • Find 2 numbers whose sum is the middle coefficient, and whose product is the last term. • Check by foiling the factors. + = 7 x = 10 ex. common factor? 5, 2 ex. + = 1 x = -20 common factor? -4, 5

  20. Lets take a look at x2 + 5x + 6 • Create a rectangle using the exact number of tiles in the given expression. • Remember that a trinomial represents area – two binomials multiplied together. • What is the width and length of the rectangle? • These are the FACTORS of the original rectangle. How could we factor this using algebra tiles? Does that make sense? (x+3)(x+2) x + 3 x + 2

  21. Using algebra tiles, factor the following… • Create a rectangle using the exact number of tiles in the given expression. • Remember that a trinomial represents area – two binomials multiplied together. • What is the width and length of the rectangle? • These are the FACTORS of the original rectangle.

  22. Homework Time!

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