Ex.12.1 Q2 Algebraic Expressions Solution - NCERT Maths Class 7

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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 \(0.2, q, q\)

  
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