I was given a problem in my pre-univeristy Calculus class, and I can't find the coeffecients. The problem is (1-2x)^3 = ax^3 + bx^2 + cx + d. I know that the coefficient of d is 1, and I know that the degree is 3. But I have no idea how to find the coefficients of a, b, and c. Please help.
Finding Coefficients in Standard Form: (1-2x)^3 = ax^3 + bx^2 + cx + d
- Thread starter Benjiman
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Dr.Peterson
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If you don't know the formula for (a+b)^3, you can take the slow way and expand(1-2x)^3 by first finding (1-2x)^2 = (1-2x)(1-2x), and then multiplying that by (1-2x). Then just match up the coefficients.
Please show us some work, so we can tell what level of help you need beyond this.
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Try using what you learned back in algebra. Multiply (1 - 2x) by (1 - 2x). Then multiply the result by (1 - 2x). (here) Simplify the result by combining all "like" terms. (here)
Then compare the coefficients of each term. Whatever is the coefficient on the cubed-x term in your expansion of the left-hand side, this will be the value of "a". And so forth.
If you get stuck, please reply with a clear listing of your efforts so far. Thank you!
