NCERT Solutions for Class 9th Maths Chapter 2 Think and Reflect — Introduction (Example 3)

Book page 17 Updated on2026-09-08

Q1.

Can you identify the terms, variables and coefficients of this algebraic expression?

Answer

The expression is the area of the bent-wire rectangle, 10x − x².

Part	What it is here
Terms	10x and −x²
Variable	x only (the length in cm)
Coefficients	10 of x, −1 of x²
Constant term	none (it is 0)
Degree	2 — the highest power of x present

Why it happens: the area is x(10 − x). Expanding the bracket gives 10x − x², and the minus sign belongs to the term, so the coefficient of x² is −1, not 1. The constant is 0 because a rectangle of zero length has zero area.

Tip: Always read a coefficient with its sign. Writing “the coefficient of x² is 1” here would change the expression completely.

Q2.

Can you point out any similarity or difference between the algebraic expressions obtained in Examples 1 and 3?

Answer

Similarity: both are algebraic expressions — sums of terms, each term a number multiplying letters.

Differences:

	Example 1: 4x + 5y + 3	Example 3: 10x − x²
Number of variables	two (x, y)	one (x)
Highest power	1	2
Constant term	3	none
Univariate polynomial?	no — two variables	yes, of degree 2

Why it matters: this is exactly the split the chapter is about to make. Expressions with a single variable and its powers are the ones we call univariate polynomials, and only those get a degree. 10x − x² qualifies; 4x + 5y + 3 does not, because it needs two independent letters.

Check it yourself: in Example 1 you can double x and leave y alone. In Example 3 there is only one dial to turn — fix x and the whole rectangle, and its area, is fixed.

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