Posted by Jay on Monday, June 6, 2011 at 10:58pm.
Can somebody explain to me why equating coefficients work?
Example:
8x^3+13x = Ax^3 + 2Ax + Bx^2 + 2B + Cx + D
expanded into:
8x^3 + 13x = Ax^3 + Bx^2 + (2A+C)x + 2(B+D)
where A,B,C,D are constants.
Why does 8 = A; 0 = B; 13 = 2A + C; etc.
I know they have same power variables, but why does this actually work? Thanks!

calculus(equating coefficients)  MathMate, Tuesday, June 7, 2011 at 12:20am
8x^3+13x ≡ Ax^3 + 2Ax + Bx^2 + 2B + Cx + D ...(1)
=>
(8A)x^3Bx²+(132AC)x (2B+C)≡ 0 ...(2)
This is an identity, and has to work for all values of x.
This can happen if and only if the coefficients on the lefthand side of (2) are zero, which then implies
8A=0, or A=8,
etc.
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