Multiplication of Trinomials Elvira Scotto-Padavano Middletown High School.

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Presentation transcript:

Multiplication of Trinomials Elvira Scotto-Padavano Middletown High School

New York State Math 8 8.PS.1 Use a variety of strategies to understand new math content and to develop more efficient methods 8.R.4 Explain how different representations express the same relationship 8.A.8 Multiply a binomial by a monomial or a binomial (integer coefficients)

Multiplying Binomials Two Digit Multiplication FOIL Double Distributive Property of Multiplication over Addition Algebra Tiles Area Rugs

Multiplying Binomials 11 X 23

Two Digit Multiplication 11 X x + 1 X 2x x +3 2x 2 +2x 2x 2 + 5x + 3

Two Digit Multiplication 5x – 3 2x x x 2 – 6x 10x 2 – x - 3

Multiply X – 7 3X + 2

FOIL First Outer Inner Last First ( 1x + 1 )( 2x + 3 ) 1x times 2x = 2x 2 Outer ( 1x + 1 )( 2x + 3 ) 1x times +3 = +3x Inner ( 1x + 1 )( 2x + 3 ) +1 times 2x = +2x Last ( 1x + 1 )( 2x + 3) +1 times +3 = +3 Answer 2x 2 + 5x + 3

FOIL Multiply ( 2x - 5 ) ( x – 7 ) 2x 2 – 14x – 5x x 2 – 19x + 35

FOIL Multiply ( 3x – 5) ( 2x + 6)

Double Distributive Property of Multiplication over Addition ( 1x + 1)( 2x + 3) 1x ( 2x + 3 ) + 1( 2x + 3 ) 2x 2 + 3x + 2x + 3 2x 2 + 5x + 3

Double Distributive Property of Multiplication over Addition Multiply ( x + 9 ) ( 3x + 4) x ( 3x + 4 ) + 9 ( 3x + 4) 3x 2 + 4x + 27x x x + 36

Double Distributive Property of Multiplication over Addition Multiply ( 5x + 6) ( 3x - 11)

Algebra Tiles Homemade Tiles Virtual Algebra Tiles

Area Rugs Similar to algebra tiles No manipulatives or computers needed Student generated and drawn

Area Rug x +2 x+7 x2x2 +2x+14 +7x X 2 + 9x +14

Area Rugs x x x2x2 -8x +3x-24 X 2 – 5x - 24

Area Rugs Use an area rug to find the product of ( 2x + 3 )( x + 1) 2x +3 x +1 2x 2 + 5x + 3

Recap Multiplication Find the product of ( 2x – 3 ) ( x + 2)

QUESTIONS ????????? Which method do you prefer?