Question 63563: Use Pascal's Triangle to expand each binomial.
(a-b)^6
Answer by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! QUESTION:
Use Pascal's Triangle to expand each binomial.
(a-b)^6
ANSWER:
Pascal's Triangle.
It is a triangle of numbers, which is given below:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
1 7 21 35 35 21 7 1
1 8 28 56 70 56 28 8 1
1 9 36 84 126 126 84 36 9 1
Each number in the triangle is the sum of two above. For example, the 6 on line 5 is the sum of the pair of 3's above. So the next line is
1, 10 (1 + 9), 45 (9 + 36), 120 (36 + 84), etc.
Study these numbers and see if you can figure what the next line should be before reading on . . .
Your question.
(x-y)^6
Seventh raw of the triangle gives,COEFFIECIENTS OF THE EXPANSION.
That is, 1 6 15 20 15 6 1
And the variable terms will come like this,
x^6
x^5 * y^1
x^4* y^2
x^3 * y^3
x^2 * y^4
x^1 * y^5
y^6
(power of the first term will decrease while power of second term will increase till it is 6.)
Since here it is (x - 6), the sign of the term will be alternatively positive and negative like this,
+, -, + , -, +, -, +, - , +, ...................
(x-y)^6= 1x^6+ 6x^5 y^1+ 15x^4 y^2+20x^3 y^3+ 15x^2 y^4+ 6x^1 y^5+ 1y^6
which is the answer to your question.
Hope you understood.
Regards.
praseenakos@yahoo.co.in
|
|
|
