9.2 Multiplying Polynomials fguilbert.

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Presentation transcript:

9.2 Multiplying Polynomials fguilbert

Review - Simplify x2 - 2x + 5x2 - 4x 2x2 - 5x + x2 +3x-7 3x + 2y + 5x - 4y x2 - 2x + 5x2 - 4x 2x2 - 5x + x2 +3x-7 7a + 5b- (3a + b) fguilbert

combine like terms answers 3x + 2y + 5x - 4y 8x - 2y x2 - 2x + 5x2 - 4x 6x2 - 6x combine like terms fguilbert

answers 2x2 -5x + x2 +3x -7 3x2 - 2x - 7 7a + 5b - (3a + b) fguilbert

Objective To multiply monomials and binomials. To use the FOIL method to expand two binomials. fguilbert

A monomial has 1 term. -3 X 5X2 monorail 1 rail fguilbert

A binomial has 2 unlike terms. 2X - 3 x + b X2 - X n + 3 bicycle fguilbert bicycle

A trinomial has 3 unlike terms. x2 + 2x - 5 x + xy + y fguilbert triangle 3 sides

Multiply x ( 4x ) = 4 X2 3 ( 5x ) = 15 x fguilbert

Distribute = 5x2 + 10x 5x ( X + 2) -3 (X - 2) = -3X + 6 fguilbert

Tile models can be used to visualize a product. Think of area. fguilbert

X A = l w x•x = x2 X X2 x 1•x = x 1 X fguilbert 1 1 1•1= 1 1

+ + A = (X + 2)(X + 3) Find an eq. for this tile model of area. 3 x x fguilbert A = (X + 2)(X + 3)

(X + 3)(X +2) F O I L to multiply O uter F irst L ast I nner fguilbert

(X + 3)(X +2) F O I L X2 F +2X O +3X I +6 L fguilbert X2 + 5X + 6

X X X + X2 + x 111 (X+2)(X+3)=X2+5X+6 The product matches the model. 3 fguilbert

Draw an area tile model to show: ( X + 1)( X + 4 ) x +4 Your Turn x + 1 draw the lines fguilbert

A = (X + 1)(X + 4) + 4 x x + fguilbert 1

(X + 1)(X + 4) X2 First +1X Inner +4 Last +4X Outer X2 + 5X + 4 Expand fguilbert X2 + 5X + 4

Expand (x + 3)(x -5) F O I L -15 +3X X2 -5X fguilbert X2 - 2X - 15

Expand (x + 3)2= (x +3)(x + 3) x2 +3x + 3x + 9 x2 +6x + 9 fguilbert

Expand (x + 4)(x - 3) First x2 Outer -3x Inner 4x Last -12 = x2 - 3x + 4x - 12 = x2 + x -12 Your Turn fguilbert

X2 -3X -2X +6 = X2 - 5X + 6 Multiply (x - 2)(x - 3) foiled again ! fguilbert

Find (3x -2)(2x +3) F 6X2 O +9X I -4X L -6 = 6X2 +5X - 6 fguilbert

( 5 + √7 ) (√7 - 2) = F O I L _ _ 5 √7 - 10 + 7 - 2 √7 = _ _ ( 5 + √7 ) (√7 - 2) = F O I L _ _ 5 √7 - 10 + 7 - 2 √7 = combine like terms 3 √7 - 3 fguilbert

You try these (2x + 5) (x - 2)= (w + 3) (w - 3)= fguilbert

(2x + 5) (x - 2) 2x2 - 4x + 5x - 10 = First Outer Inner Last fguilbert

(w + 3) (w - 3) = w2 – 3w + 3w - 9 = w2 - 9 fguilbert

(3 - 5rs) (2r + 5s) = 6r + 15s - 10r2s - 25rs2 Last one Curses ! Foiled Again fguilbert

Do your homework! The key to freedom is courage. fguilbert