Simplify the expression $(4 p^{2} + 3 p) - (p^{2} - 5 p + 2)$ and choose the correct simplified form.

easy MCQ 1 mark Class 8 · Mathematics · Algebraic Expressions and Identities

Answer

3 p^{2} + 8 p - 2

The correct answer is $3 p^{2} + 8 p - 2$ — The resulting simplified expression is $3 p^{2} + 8 p - 2$ .

Step-by-step solution

Distribute the negative sign to each term inside the second parentheses: subtract $p^{2}$ , add $5 p$ , subtract $2$ .
Combine like terms: $4 p^{2} - p^{2} = 3 p^{2}$ , $3 p + 5 p = 8 p$ , and the constant remains $- 2$ .
The resulting simplified expression is $3 p^{2} + 8 p - 2$ .

Common mistake: Forgetting to change signs when expanding the second parentheses

Concept tested: Simplification of polynomial expressions