NCERT · Class 8 · Mathematics · FactorisationFactorise: $p^2 + 6p + 9$
Step-by-Step Solution
The given expression is $p^2 + 6p + 9$. We can write it as $p^2 + 2(p)(3) + 3^2$. This is of the form $a^2 + 2ab + b^2 = (a + b)^2$. Here, $a = p$ and $b = 3$. Thus, it factorises to $(p + 3)(p + 3)$. Therefore, the correct option is $(p + 3)^2$.
Detailed Options Breakdown
Option : (p - 3)(p - 3)
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Factorisation.
Option 1: (p + 3)(p + 3) (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: (p + 9)(p + 1)
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Factorisation.
Option 3: (p + 3)(p - 3)
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Factorisation.
💡 Study Guide: This question tests core syllabus concepts from Factorisation. For formulas, key summaries, and mock exam reference guides, read the full Factorisation Revision Notes.