Math Problem Statement
Solution
The given expression is:
We need to find the values of and .
Step 1: Expand the left-hand side
We'll first expand .
Start by expanding :
Now, multiply this by :
Step 2: Collect like terms
Group the terms by powers of :
Step 3: Compare coefficients with the right-hand side
Now, compare this with the right-hand side .
- Coefficient of :
- Coefficient of :
- Coefficient of :
- Constant term:
Step 4: Solve for and
-
From the constant term equation:
-
Substitute into the equation for :
-
Verify with the equation for :
Thus, the values of and are:
Would you like further details or have any questions?
Related Questions:
- How do we expand binomials in general?
- What are other ways to solve for unknowns in polynomial identities?
- Can this problem be solved using synthetic division?
- How does comparing coefficients help in solving polynomial equations?
- What are some typical uses of this method in algebra?
Tip:
When expanding products of polynomials, always group terms by powers of for easier comparison with the target expression.
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomial Expansion
Comparing Coefficients
Formulas
(ax + 1)(x - 3)(x + b)
Polynomial expansion
Theorems
Polynomial identities
Comparing coefficients
Suitable Grade Level
Grades 9-12
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