CBSE Class 7 - Mathematics - Chapter – 12 - Algebraic Expressions - NCERT Solution 12.1 (#NCERTAnswers)

Chapter – 12 - Algebraic Expressions
NCERT Exercise 12.1

Question 1: Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:

(i) Subtraction of z from y .
(ii) One-half of the sum of numbers x and y .
(iii) The number z multiplied by itself.
(iv) One-fourth of the product of numbers p and q .
(v) Numbers x and y both squared and added.
(vi) Number 5 added to three times the product of m and n .
(vii) Product of numbers y and z subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.


Answer:
(i) y - z

(ii)
(x+y)
-----
 2

(iii)  z²

(iv)  pq
     ----
       4

(v)   x² + y²

(vi) 3mn + 5

(vii) 10 - yz

(viii) ab - ( a + b )




Question 2:
(i) Identify the terms and their factors in the following expressions, show the terms and factors by tree diagram:
(a) x - 3
(b) 1 + x + x²
(c) y - y³
(d) 5xy² + 7x²y
(e) -ab + 2b² - 3a²

(ii) Identify the terms and factors in the expressions given below:
(a)  -4 x + 5
(b)  -4 x + 5y
(c)  5y + 3y²
(d) xy + 2x²y²
(e) pq + q
(f) 1.2ab - 2.4b + 3.6a
(g) ¾x + ¼
(h) 0.1p² + 0.2q²


Answer:
(i)
(a)     x - 3
          ↙   ↘
Terms    x    -3
        ↙  ↘   ↙  ↘
Factors 1  x  -1  3
 

(ii)

(a) -4 x + 5
Terms: -4x, 5
Factors: -4, x; 5

(b)  -4 x + 5y
Terms: -4x, 5y
Factors: -4, x; 5, y

(c) 5y + 3y²
Terms: 5y, 3y²
Factors: 5,y; 3,y,y

(d) xy + 2x²y²
Terms: xy, 2x²y²
Factors: x,y; 2,x, x, y, y

(e) pq + q
Terms: pq, q
Factors: p,q; q

(f) 1.2ab - 2.4b + 3.6a
Terms:1.2ab, -2.4b, 3.6a
Factors: 1.2, a, b;
-2.4, b;
3.6, a

(g) ¾x + ¼
Terms: ¾x, ¼
Factors: ¾,x; ¼

(h) 0.1p² + 0.2q²
Terms: 0.1p², 0.2q²
Factors: 0.1,p,p; 0.2, q, q


Question 3:
Identify the numerical coefficients of terms (other than constants) in the following expressions:

(i) 5 – 3t² (ii) 1 + t + t² + t³
(iii) x + 2xy + 3y² (iv) 100m + 1000n
(v) – p²q² + 7pq (vi) 1.2 a + 0.8 b
(vii) 3.14r² (viii) 2(l + b)
(ix) 0.1 y + 0.01y²


Answer:
Expression Terms Coefficients
(i) 5 – 3t² –3t²      -3

(ii) 1 + t + t² + t³ t 1
t² 1
t³ 1

(iii) x + 2xy + 3y² x 1
2xy 2
3y² 3

(iv) 100m + 1000n 100m 100
1000n 1000

(v) – p²q² + 7pq – p²q² 1
7pq 7

(vi) 1.2 a + 0.8 b 1.2a 1.2
0.8b 0.8

(vii) 3.14r² 3.14r² 3.14

(viii) 2(l + b)
= 2l + 2b 2l 2
2b 2

(ix) 0.1 y + 0.01y² 0.1y 0.1
0.01y² 0.01


Question 4:

(a) Identify terms which contain x and give the coefficient of x.
(i) y²x + y
(ii) 13y² – 8yx
(iii) x + y + 2
(iv) 5 + z + zx
(v) 1 + x + xy
(vi) 12xy² + 25
(vii) 7x + xy²

(b) Identify terms which contain y 2 and give the coefficient of y² .
(i) 8 – xy²
(ii) 5y² + 7x
(iii) 2x²y – 15xy² + 7y²


Answer:
(a) Expression Terms with factor x Coefficient of x

(i) y²x + y y²x y²

(ii) 13y² – 8yx –8yx -8y

(iii) x + y + 2 x 1

(iv) 5 + z + zx zx z

(v) 1 + x + xy x 1
xy y

(vi) 12xy² + 25 12xy² 12y²

(vii) 7x + xy² 7x 7
xy² y²

(b) Expression Terms contain y² Coeeficient of y²

(i) 8 – xy² –xy² – x

(ii) 5y² + 7x 5y² 5

(iii) 2x²y – 15xy² + 7y² – 15xy² –15x
7y² 7

Question 5:  Classify into monomials, binomials and trinomials.
(i) 4y – 7z (ii) y² (iii) x + y – xy
(iv) 100 (v) ab – a – b (vi) 5 – 3t
(vii) 4p²q – 4pq² (viii) 7mn (ix) z² – 3z + 8
(x) a² + b² (xi) z² + z (xii) 1 + x + x²

Answer:
(i) 4y – 7z Binomial
(ii) y² Monomial
(iii) x + y – xy Trinomial
(iv) 100 Monomial
(v) ab – a – b Trinomial
(vi) 5 – 3t Binomial
(vii) 4p²q – 4pq² Binomial
(viii) 7mn Monomial
(ix) z² – 3z + 8 Trinomial
(x) a² + b² Binomial
(xi) z² + z Binomial
(xii) 1 + x + x² Trinomial



Question 6: State whether a given pair of terms is of like or unlike terms.
(i) 1, 100

(ii) –7x, 5x
 ---
 2

(iii) – 29x, – 29y

(iv) 14xy, 42yx

(v) 4m²p, 4mp²

(vi) 12xz, 12x²z²


Answer:
Pair of Terms Like or Unlike
(i) 1, 100 Like terms

(ii) –7x, 5x Like terms
 ---
 2

(iii) – 29x, – 29y Unlike terms

(iv) 14xy, 42yx Like terms

(v) 4m²p, 4mp² Unlike terms

(vi) 12xz, 12x²z² Unlike terms


Question 7:
Identify like terms in the following:
(a) – xy², – 4yx² , 8x², 2xy², 7y, –11x², – 100x, – 11yx, 20x²y, –6x², y, 2xy, 3x
(b) 10pq, 7p, 8q, –p²q², –7qp, –100q, –23, 12q²p², –5p², 41, 2405p, 78qp, 13p²q, qp², 701p²


Answer:
(a) Like terms are:
(i) -xy², 2xy² (ii) -4yx²,20x²y
(iii) 8x², -11x², -6x² (iv) 7y , y
(v) -100x, 3x (vi) -11yx, 2xy

(b) Like terms are:
(i) 10pq, -7pq, 78pq (ii) 7p, 2405p
(iii) 8q, -100q (iv) -p²q² ,12p²q²
(v) -12,41 (vi) -5p²,701p²
(vii) 13 p²q, qp²