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INSTRUCTORS Carleen Eaton Grant Fraser Eric Smith
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For more information, please see full course syllabus of Algebra 1
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Lecture Comments (3)

0 answers

Post by David Duque Henao on August 20, 2013

Foil method is the same thing as distributive property, isn´t it?

1 answer

Last reply by: Dr Carleen Eaton
Mon Feb 7, 2011 5:27 PM

Post by Victor Felix on January 24, 2010

it was mistake + 35y instead 53

Multiplying Polynomials

  • Use the distributive property to multiply one polynomial by another polynomial.
  • You can use the FOIL method to multiply one binomial by another binomial. But it is best to avoid relying on the FOIL method. Instead, get used to multiplying two binomials by using the distributive property.

Multiplying Polynomials

Multiply:
( 2x + 4y )( 6x2 − 3xy + 5y2 )
  • ( 2x )( 6x2 ) + ( 2x )( − 3xy ) + ( 2x )( 5y2 ) + ( 4y )( 6x2 ) + ( 4y )( − 3xy ) + ( 4y )( 5y2 )
  • 12x3 − 6x2y + 10xy2 + 24x2y − 12xy2 + 20y3
12x3 + 18x2y − 2xy2 + 20y3
Multiply:
( 3j − 7k )( 5j2 + 2jk − k2 )
  • ( 3j )( 5j2 ) + ( 3j )( 2jk ) + ( 3j )( − k2 ) + ( − 7k )( 5j2 ) + ( − 7k )( 2jk ) + ( − 7k )( − k2 )
  • 15j3 + 6j2k − 3jk2 − 35j2k − 14jk2 + 7k3
15j3 − 29j2k − 17k2 + 7k3
Multiply:
( 6x2 − 4x + 10 )( 4x2 + 3x + 5 )
  • ( 6x2 )( 4x2 ) + ( 6x2 )( 3x ) + ( 6x )( 5 ) + ( − 4x )( 4x2 ) + ( − 4x )( 3x ) + ( − 4x )( 5 ) + ( 10 )( 4x2 ) + ( 10 )( 3x ) + ( 10 )( 5 )
  • 24x4 + 18x3 + 30x − 16x3 − 12x2 − 20x + 40x2 + 30x + 50
24x4 + 2x3 + 28x2 + 40x + 50
Multiply:
( 8r2 + 10r − 4 )( 3r2 − 2r − 1 )
  • ( 8r2 )( 3r2 ) + ( 8r2 )( − 2r ) + ( 8r2 )( − 1 ) + ( 10r )( 3r2 ) + ( 10r )( − 2r ) + ( 10r )( − 1 ) + ( − 4 )( 3r2 ) + ( − 4 )( − 2r ) + ( − 4 )( − 1 )
  • 24r4 − 16r3 − 8r2 + 30r3 − 20r2 − 10r − 12r2 + 8r + 4
24r4 + 14r3 − 40r2 − 2r + 4
Multiply:
( 4x − 5 )( 8x + 7 )
  • Foil:( 4x )( 8x ) + ( 4x )( 7 ) + ( − 5 )( 8 ) + ( − 5 )( 7 )
  • 32x2 + 28x − 40 − 35
32x2 + 28x − 75
Multiply:
( 6p + 12 )( 10p − 8 )
  • ( 6p )( 10p ) + ( 6p )( − 8 ) + ( 12 )( 10p ) + ( 12 )( − 8 )
  • 60p2 − 48p + 120p − 96
60p2 + 120p − 144
Multiply:
( c − 12 )( 3c + 2 )
  • ( c )( 3c ) + ( c )( 2 ) + ( − 12 )( 3c ) + ( − 12 )( 2 )
  • 3c2 + 2c − 36c − 24
3c2 − 34c − 24
Multiply:
( 5a + 6b )( 7a − 9b )
  • ( 5a )( 7a ) + ( 5a )( − 9b ) + ( 6b )( 7a ) + ( 6b )( − 9b )
  • 35a2 − 45ab + 42ab − 54b2
35a2 − 3ab − 54b2
Multiply:
( 12x − 8y )( 9x − 11y )
  • ( 12x )( 9x ) + ( 12x )( − 11y ) + ( − 8y )( 9x ) + ( − 8y )( − 11y )
  • 108x2 − 132xy − 72xy + 88y2
108x2 − 204xy + 88y2
Multiply:
( 4m − 9n )( 7m + 6n )
  • ( 4m )( 7m ) + ( 4m )( 6n ) + ( − 9n )( 7m ) + ( − 9n )( 6n )
  • 28m2 + 24mn − 63mn − 54n2
28m2 − 39mn − 54n2

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Multiplying Polynomials

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Distributive Property 0:08
    • Example
  • FOIL Method 2:44
    • First, Outer, Inner, Last
  • Example 1: Multiply 5:32
  • Example 2: Multiply 7:27
  • Example 3: Multiply 9:41
  • Example 4: Multiply 13:56