1 / 22

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.

laith-nunez
Télécharger la présentation

Multiplying Two Binomials

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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!

More Related