Question

Find the value of \(2a^3 - [3a^3 + 4a^2 - \{2a^3 - 7a^3\} + 5a^3 - 7a^2]\).

• A. \(-11a^3 + 3a^2 \)
• B. \(7a^2 + 3a^3 \)
• C. \(11a^3 - 3a^2 \)
• D. \(-11a^3 - 3a^2 \)

Hint:

While simplifying algebraic expressions: - Always remove brackets carefully (watch for negative signs) - Combine like terms step-by-step - Avoid doing everything in one step to prevent sign errors

Answer 1

The Correct Option is A

Concept: Group like terms ($a^3$ with $a^3$, and $a^2$ with $a^2$) and carefully distribute the negative sign through the brackets.
Step 1: Simplify the innermost braces.
\(\{2a^3 - 7a^3\} = -5a^3\)

Step 2: Simplify the square brackets.
\([3a^3 + 4a^2 - (-5a^3) + 5a^3 - 7a^2]\)
\(= [3a^3 + 4a^2 + 5a^3 + 5a^3 - 7a^2]\)
\(= [(3+5+5)a^3 + (4-7)a^2] = [13a^3 - 3a^2]\)

Step 3: Subtract from the first term.
\(2a^3 - [13a^3 - 3a^2] = 2a^3 - 13a^3 + 3a^2 = -11a^3 + 3a^2\).