Math Problem Statement
(a - 3b)^2 - (a + b)^2
Solution
Let's solve the given expression:
Step 1: Expand both squares
For , use the expansion formula :
For , use the expansion formula :
Step 2: Subtract the two expanded forms
Now, subtract from :
Distribute the negative sign:
Step 3: Combine like terms
Cancel out and combine the remaining terms:
Step 4: Final Answer
Thus, the simplified expression is:
This matches option A in the provided choices.
Would you like further details on any step?
Here are some related questions to practice:
- How do you expand binomials using the square of a sum or difference formula?
- What is the general formula for and ?
- How do you simplify expressions with like terms?
- Can you expand and simplify ?
- How does changing the signs of terms in a binomial affect the result?
Tip: When simplifying expressions involving squares of binomials, always expand each term separately before combining like terms.
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Math Problem Analysis
Mathematical Concepts
Algebra
Binomial Expansion
Difference of Squares
Formulas
(x - y)^2 = x^2 - 2xy + y^2
(x + y)^2 = x^2 + 2xy + y^2
Theorems
Binomial Expansion Theorem
Suitable Grade Level
Grades 8-10