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8.3 MULTIPLYING BINOMIALS:

Distributive Property: for any real numbers a, b, c, and d:. 8.3 MULTIPLYING BINOMIALS:. a c. + b c. + a d. ( a + b )( c + d )=. + b d. FOIL METHOD: for any real numbers a, b, c, and d in ( a + b )( c + d ):. 8.3 MULTIPLYING BINOMIALS:. F IRST: ( a )( c ) = a c.

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8.3 MULTIPLYING BINOMIALS:

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  1. Distributive Property: for any real numbers a, b, c, and d: 8.3 MULTIPLYING BINOMIALS: ac +bc +ad (a+b)(c+d)= +bd

  2. FOIL METHOD: for any real numbers a, b, c, and d in (a+b)(c+d): 8.3 MULTIPLYING BINOMIALS: FIRST: (a)(c) = ac OUTER: (a)(d) = ad = ac+ad+bc+bd INNER: (b)(c) = bc LAST: (b)(d) = bd

  3. GOAL:

  4. MULTIPLYING BINOMIALS: When multiplying polynomials we must keep in mind the laws of exponents from chapter 7 and the distributive property. Ex: What is the simplest form of: (2x+4)(3x– 7)?

  5. FOIL METHOD: (2x+4)(3x– 7)? FIRST: (2x)(3x) = 6x2 6x2-14x+12x-28 OUTER: (2x)(-7) = -14x INNER: (4)(3x) = 12x 6x2-2x-28 LAST: (4)(-7) = -28 The simplest form is: 6x2-2x-28

  6. MULTIPLYING BINOMIALS: We can also use a table to: 6x2 12x -14x -28 6x2+12x-14x-28 6x2-2x-28

  7. REAL-WORLD: What is the area of the frame? 5x-2 7x+1

  8. SOLUTION: Using the FOIL method, table or distributive property: 5x-2 Area = b.h Area = (7x+1)(5x-2) 7x+1 Area = 35x2-14x+5x-2 Total area = 35x2-9x-2

  9. REAL-WORLD: A factory is looking into making the new label of a can of soup.The can needs to have the dimensions shown in the sketch.what is the total amount of paper needed to make a label?

  10. SOLUTION: The label will need to be a rectangle, but the length of the label is the circumference of the can (2πr): x + 4 =2π(x+1) 2πr =2πx+2π Area = b.h Area = (2πx+2π)(x+4) Area = 2πx2+8xπ+2πx+8π Total paper needed = 2πx2+10xπ+8π

  11. VIDEOS: Polynomials Multiplying Multiplying: https://www.khanacademy.org/math/trigonometry/polynomial_and_rational/polynomial_tutorial/v/multiplying-polynomials

  12. CLASSWORK:Page 489-490: Problems: As many as needed to master the concept

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