Triangle
Who was Pascal’s triangle named after?
Blaise pascal
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The top rows' expression is (x + y) raised to which power?
0
Where are the 1’s placed?
On both left and right edges of every row
(x+1)^2
x^2+2x+1
How many terms does (x+1)^39 have?
40 terms.
What number do you start with on the top of the triangle?
1
What would be the expression for the fourth row?
(a+b)^4
What are the coefficients of the second row?
1 1
(x+1)^3
x^3+3x^2+3x+1
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What pattern do you notice in Pascal's Triangle? (besides the 1's)
Add the numbers above to give you the number below.
What what would be the expression for the 10th row?
(a+b)^10
What are the coefficients for the 4th row?
1 4 6 4 1
(x+2)^3
x^3+6x^2+12x+8
Can we build the triangle, or do we need to memorize it?
We can build it!
Is the triangle symmetric?
Yes
Does it matter which value is a or b in Pascal's Triangle?
No, but your answer will be backwards if you switch!
Find the next row of Pascal's Triangle
1 4 6 4 1
1 5 10 10 5 1
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What is Pascal's Triangle used for?
It is used to give coefficients when you are multiplying binomials.
Do x-values count up or down using Pascal's Triangle?
Down
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What row of Pascal's Triangle is this?
1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1
(x-1)^2
x^2 -2x + 1