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If (1 + 2x)^5+ (1 - 2x)^5 = a + bx + cx?
find the values of the constants a, b and c.

1 Answer

6 votes

Answer:

steps below

Explanation:

5th level of Pascal triangle: 1,5,10,10,5,1

(1+2x)⁵ = 1*1⁵*(2x)⁰+5*1⁴*2x+10*1³*(2x)²+10*1²*(2x)³+5*1¹(2x)⁴+1*1⁰*(2x)⁵

= 1 + 10x + 40x² + 80x³ + 80x⁴ + 32x⁵ .. (1)

(1-2x)⁵ = 1 - 10x + 40x² - 80x³ + 80x⁴ - 32x⁵ .. (2)

(1)+(2): (1+2x)⁵ + (1-2x)⁵ = 160x⁴ + 80x² +2

a + bx + cx ?? suppose it's ax⁴ + bx² + cx, if you have other set up.. adjust by yourself

a = 160, b = 80, c = 2

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