NCERT Solutions for Class 9th Maths Chapter 2 Think and Reflect — Introduction

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 total cost of the garden in Example 2, 200l + 160w + 50lw.

Part	What it is here
Terms	200l, 160w, 50lw
Variables	l (length in m) and w (width in m)
Coefficients	200 of l, 160 of w, 50 of lw
Constant term	none — every term contains a variable

Why it happens: each coefficient is a rate, and reading it off tells you where it came from. The wire runs along both lengths, so 2 × ₹100 = ₹200 per metre of length; the wooden fence runs along both widths, so 2 × ₹80 = ₹160 per metre of width. The seed is charged by area, and the area is l × w, which is why the third term carries the product lw and not l or w alone.

Tip: The coefficient of a term is everything except the letters. In 50lw the coefficient is 50, and both l and w are variables of that single term.

Q2.

How is it different from the algebraic expression in Example 1?

Answer

Example 1 gave 4x + 5y + 3. Example 2 gives 200l + 160w + 50lw. Two differences matter.

The highest power. In 4x + 5y + 3 every variable appears to the power 1 and no term mixes the two letters. In 200l + 160w + 50lw the term 50lw multiplies the two variables together, so that term has degree 1 + 1 = 2.
The constant. 4x + 5y + 3 has the constant term 3 (the free pens). The garden expression has no constant — if the garden shrinks to nothing, the cost is 0.

Why it happens: the difference is not cosmetic, it is about how the quantities behave. Doubling the garden’s length doubles the wire cost, but doubling both length and width multiplies the seed cost by four, because area grows with the product. An expression in which the variables only ever appear singly, to the first power, describes something that grows in step with its inputs; a product term does not.

Did you know? A term such as 50lw is called a second-degree term, since the powers of the variables in it add to 2. Because of it, the garden expression is not linear, even though the first two terms are.

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