Ex.12.1 Q2 Algebraic Expressions Solution - NCERT Maths Class 7
Question
(i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.
(a) \(x – 3\)
(b) \(1 + x + x^2\)
(c) \(y – y^3\)
(d) \(5xy^2 + 7x^2y\)
(e) \(– ab + 2b^2 – 3a^2\)
(ii) Identify terms and factors in the expressions given below:
(f) \(–4x + 5\) (b) \(–4x + 5y\) (c) \(5y + 3y^2\)
(g) \(xy + 2x^2y^2\) (e) \(pq + q\) (f) \(1.2 ab – 2.4 b + 3.6 a\)
(h) \(\frac{3}{4}x + \frac{1}{4}\) (h) \(0.1 p^2 + 0.2 q^2\)
Text Solution
(i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.
(a) \(x – 3\)
Steps:
Term \(= x\) and Factor \(= 1\)
(b) \(1 + x + x^2\)
^{}
Steps:
Term \(= x\) and Factor \(= 1;\) Term \(= x^2\) and Factor \(= 1\)
(c) \(y – y^3\)
^{}
Steps:
Term \(= y\) and Factor \(= 1;\) Term \(= y^3\) and Factor \(= –1\)
(d) \(5xy^2 + 7x^2y\)
Steps:
Term \(= xy^2\) and Factor \(= 5;\) Term \(= x^2y\) and Factor \(= 7\)
(e) \(– ab + 2b^2 – 3a^2\)
^{}
Steps:
Term \(= ab\) and Factor \(= –1; \)Term \(= b^2\) and Factor \(= 2;\) Term \(a^2\) and Factor \(= –3\)
(ii) Identify terms and factors in the expressions given below:
(f) \(–4x + 5\) (b) \(–4x + 5y\) (c) \(5y + 3y^2\)
(g) \(xy + 2x^2y^2\) (e) \(pq + q\) (f) \(1.2 ab – 2.4 b + 3.6 a\)
(h) \(\frac{3}{4}x + \frac{1}{4}\) (h) \(0.1 p^2 + 0.2 q^2\)
S.No. |
Expression |
Term |
Factors |
a) |
\(–4x + 5\) |
\(-4x\) and \(5\) |
\(-4, x\)and \(5\) |
b) |
\(-4x + 5y\) |
\(-4x\) and \(5y\) |
\(-4, x\) and \(5, y\) |
c) |
\(5y + 3y^2\) |
\(5y\) and \(3y^2\) |
\(5, y \) and \(3, y, y\) |
d) |
\(xy + 2x^2y^2\) |
\(xy\) and \(2x^2y^2\) |
\(x, y\) and \(2, x, x,y, y\) |
e) |
\(pq + q\) |
\(pq\) and \(q\) |
\(p, q\) and \(q\) |
f) |
\(1.2ab - 2.4b + 3.6a\) |
\(1.2ab, -2.4b\) and \(3.6a\) |
\(1.2, a, b, -2.4, b\) and \(3.6, a\) |
g) |
\(\frac{{3}}{4} x + \frac{{1}}{4} \) |
\(\frac{{3}}{4} x \) and \( \frac{{1}}{4}\) |
\(\frac{{3}}{4}, x\) and \(\frac{{1}}{4} \) |
h) |
\(0.1 p^2 + 0.2 q^2\) |
\(0.1p^2\) and \(0.2q^2\) |
\(0.1, p, p\) and \(0.2, q, q\) |