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Transcript 
Binomial and Polynomial
Expansion
TEKS
MENU
CREDITS
TEKS
• 111.42.c.5F
Apply the Binomial Theorem for the expansion
of (a + b)n in powers of a and b for a positive
integer n, where a and b are any numbers
TITLE SCREEN
Credits
Pascal’s Triangle
owl.hlcs.org
Teks
Texas Education Agency
TITLE SCREEN
HOW TO DO
EXPANSIONS
F.O.I.L
PASCAL’S
TRIANGLE
.
QUIZ
EXAMPLES
TITLE SCREEN
Pascal’s Triangle for Binomial
Expansion
MENU
F.O.I.L.
FOIL stands for First Outside Inside Last and is
the fastest way to multiply problems like these.
(x +1)(x + 2) = x + 3x + 2
2
MENU
PERFECT SQUARES
Perfect Squares do not require the complete
F.O.I.L. process but only require the First and
Last parts to complete the expansion because
the middle terms cancel out.
(x + 2)(x - 2) = x - 4
2
MENU
FIRST
(x + 2)(x - 2) = x
2
LAST
(x + 2)(x - 2) = x - 4
2
FIRST
(x +1)(x + 2) = x
2
OUTSIDE
(x +1)(x + 2) = x + 2x
2
INSIDE
(x +1)(x + 2) = x + 2x + x
2
LAST
(x +1)(x + 2) = x + 3x + 2
2
EXAMPLE 1
EXAMPLE 2
EXAMPLE 3
EXAMPLE 4
MENU
Example 1
(x + 4)(x -1) = x
2
Example 1
(x + 4)(x -1) = x - x
2
Example 1
(x + 4)(x -1) = x - x + 4x
2
Example 1
(x + 4)(x -1) = x + 3x - 4
2
Example 2
(x + 5)(x - 5) = x
2
Example 2
(x + 5)(x - 5) = x - 25
2
Example 3
(x + 2) = x
4
4
Example 3
4
4
(x+2) =x +8x
3
Example 3
4
4
3
(x+2) =x +8x +24x
2
Example 3
4
4
3
2
(x+2) =x +8x +24x +32x
Example 3
4
4
3
2
(x+2) =x +8x +24x +32x+16
Example 4
(a + b)(c + d) = ac
Example 4
(a + b)(c + d) = ac + ad
Example 4
(a + b)(c + d) = ac + ad + bc
Example 4
(a + b)(c + d) = ac + ad + bc + bd
Quiz Time…
Perfect Square’s
Pascal’s Triangle
F.O.I.L.
MENU
Perfect Square’s
Quiz 1
MENU
QUIZ
Pascal’s Triangle
Quiz 1
MENU
QUIZ
F.O.I.L.
Quiz 1
MENU
QUIZ
Perfect Square #1
(a - 7)(a + 7)
a -14
a - 49
2a -14
2a - 49
2
MENU
2
QUIZ
TRY AGAIN
GOOD JOB
Pascal’s Triangle
(x - 5)
3
x +15x + 75x +125
x -15x + 75x -125
x + 5x +10x + 25
x - 5x +10x - 25
3
2
3
2
MENU
3
3
2
2
QUIZ
GOOD JOB
TRY AGAIN
F.O.I.L. #1
(x - 5)(x +1)
x - 5x - 5
x - 4x - 5
x - 6x - 5
2x 2 - 5x - 45
2
2
MENU
2
QUIZ
TRY AGAIN
GOOD JOB
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