Asked by Jay
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!
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!
Answers
Answered by
MathMate
8x^3+13x ≡ Ax^3 + 2Ax + Bx^2 + 2B + Cx + D ...(1)
=>
(8-A)x^3-Bx²+(13-2A-C)x -(2B+C)≡ 0 ...(2)
This is an identity, and has to work for <i>all</i> values of x.
This can happen if and only if the coefficients on the left-hand side of (2) are zero, which then implies
8-A=0, or A=8,
etc.
=>
(8-A)x^3-Bx²+(13-2A-C)x -(2B+C)≡ 0 ...(2)
This is an identity, and has to work for <i>all</i> values of x.
This can happen if and only if the coefficients on the left-hand side of (2) are zero, which then implies
8-A=0, or A=8,
etc.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.