Question 383023: What are the first 4 terms in the expansion of (3+4x)^5?
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! What are the first 4 terms in the expansion of (3+4x)^5?
coefficients (Pascal's Triangle (Binomial Expansion)):
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 5 1
powers on (x + y)^n, n + 1 terms, k = 1 to n + 1 terms
x^(n - k + 1), y^(k - 1)
(x + y)^0 = 1
(x + y)^1 = x + y
(x + y)^2 = x^2 + 2xy + y^2
(x + y)^3 = x^3 + 3(x^2)y + 3xy^2 + y^3
(x + y)^4 = x^4 + 4(x^3)y + 6(x^2)y^2 + 4xy^3 + y^4
(x + y)^5 = x^5 + 5(x^4)y + 10(x^3)y^2 + 10(x^2)y^3 + 5xy^4 + y^5
the first 4 terms of (3+4x)^5 are:
3^5, 5*3^4*4x, 10*3^3*(4x)^2, 10*3^2*(4x)^3
or 243, 5*81*4x, 10*27*16x^2, 10*9*64x^3
or 243, 1620x, 4320x^2, 5760x^3
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