Question 187505: I do not understand the process for working out problems such as (2x-5)^3.
Answer by J2R2R(94)   (Show Source):
You can put this solution on YOUR website! I do not understand the process for working out problems such as (2x-5)^3.
Pascal’s triangle which is nothing more than 11 raised to various powers but any values greater than 9 are not carried over to the next column. You add adjoining numbers to get the numbers for the next row which is easier if you have it constructed as a triangle widening equally on both sides as each number equals the sum of the two numbers above it on either side.
For the power of 0 : 1
For the power of 1 : 1,1
For the power of 2 : 1,2,1 from 1, 1+1, 1
For the power of 3 : 1,3,3,1 from 1, 1+2, 2+1, 1
For the power of 4 : 1,4,6,4,1 from 1, 1+3, 3+3, 3+1, 1
For the power of 5 : 1,5,10,10,5,1 from 1, 1+4, 4+6, 6+4, 4+1, 1
etc.
11^0 = 1
11^1 = 11
11^2 = 121
11^3 = 1331
11^4 = 14641
11^5 = 15(10)(10)51 = 161051 after carrying the tens over
etc.
So this is how you expand (a + b)^n.
For (a + b)^3 we will use coefficients 1, 3, 3, 1.
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
Therefore (2x – 5)^3 =
(2x)^3 + 3(2x)^2(-5) + 3(2x)(-5)^2 + (-5)^3 =
8x^3 – 60x^2 + 150x - 125
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