NCERT Class 7 Maths Chapter 12 Algebraic Expressions Exercise 12.1

Chapter 12 Algebraic Expressions 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.
Answer:
y - z

(ii) One-half of the sum of numbers x and y.
Answer:
1/2 (x + y) = x + y/2

(iii) The number z multiplied by itself.
Answer:
z x z = z²

(iv) One-fourth of the product of numbers p and q.
Answer:
1/4 (p x q) = pq/4

(v) Numbers x and y both squared and added.
Answer:
x² + y²

(vi) Number 5 added to three times the product of numbers m and n.
Answer:
3mn + 5

(vii) Product of numbers y and z subtracted from 10.
Answer:
10 - (y x z) = 10 - yz

(viii) Sum of numbers a and b subtracted from their product.
Answer:
(a × b) - (a + b) = ab - (a + b)

Question 2: (i) Identify the terms and their factors in the following expressions
Show the terms and factors by tree diagrams.
(a) x - 3
Answer:

Expression: x - 3
Terms: x, -3
Factors: x, -3

(b) 1 + x + x²
Answer:
Expression: 1 + x + x²
Terms: 1, x, x²
Factors: 1; x; x, x


(c) y – y³
Answer:

Expression: y – y³
Terms: y, -y³
Factors: y; -y, -y, -y

(d) 5xy² + 7x²y
Answer:

Expression: 5xy² + 7x²y
Terms: 5xy², 7x²y
Factors: 5, x, y, y; 7, x, x, y

(e) -ab + 2b² – 3a²
Answer:
Expression: -ab + 2b² – 3a²
Terms: -ab, 2b², -3a²
Factors: -a, b; 2, b, b; -3, a, a

(ii) Identify terms and factors in the expressions given below:
(a) – 4x + 5
(b) – 4x + 5y
(c) 5y + 3y²
(d) xy + 2x²y²
(e) pq + q
(f) 1.2 ab – 2.4 b + 3.6 a
(g) 3/4 x + 1/4
(h) 0.1 p2 + 0.2 q2
Answer:


Expression

Terms

Factors

(a)

- 4x + 5

-4x

5

-4, x

5

(b)

- 4x + 5y

-4x

5y

-4, x

5, y

(c)

5y + 3y²

5y

3y²

5, y

3, y, y

(d)

xy + 2x²y²

xy

2x²y²

x, y

2, x, x, y, y

(e)

pq + q

pq

q

p, q

q

(f)

1.2 ab - 2.4 b + 3.6 a

1.2ab

-2.4b

3.6a

1.2, a, b

-2.4, b

3.6, a

(g)

3/4 x + 1/4

3/4 x

¼

3/4, x

1/4

(h)

0.1 p2 + 0.2 q2

0.1p²

0.2q²

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 + 3y
(iv) 100m + 1000n
(v) – p²q² + 7pq
(vi) 1.2 a + 0.8 b
(vii) 3.14 r²
(viii) 2 (l + b)
(ix) 0.1 y + 0.01 y²
Answer:


Expression

Terms

Coefficients

(i)

5 – 3t2

- 3t²

-3

(ii)

1 + t + t2 + t3

t

1

1

1

(iii)

x + 2xy + 3y

x

2xy

3y

1

2

3

(iv)

100m + 1000n

100m

1000n

100

1000

(v)

– p2q2 + 7pq

-p²q²

7pq

-1

7

(vi)

1.2 a + 0.8 b

1.2a

0.8b

1.2

0.8

(vii)

3.14 r2

3.14r²

3.14

(viii)

2 (l + b)

2l

2b

2

2

(ix)

0.1 y + 0.01 y2

0.1y

0.01y²

0.1

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
Answer:


Expression

Terms

Coefficient of x

(i)

y2x + y

y2x

y2

(ii)

13y2 – 8yx

- 8yx

-8y

(iii)

x + y + 2

x

1

(iv)

5 + z + zx

x

zx

1

z

(v)

1 + x + xy

xy

y

(vi)

12xy2 + 25

12xy²

12y²

(vii)

7x + xy2

7x

xy²

7

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


Expression

Terms

Coefficient of y2

(i)

8 - xy2

- xy2

- x

(ii)

5y2 + 7x

5y2

5

(iii)

2x2y - 15xy2 + 7y2

- 15xy²

7y²

- 15x

7

Question 5: Classify into monomials, binomials and trinomials.
(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
(Like term)
(ii) –7x, (5/2)x (Like term)
(iii) – 29x, – 29y (Unlike terms)
(iv) 14xy, 42yx (Like term)
(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
Answer:
– xy², 2xy²
– 4yx², 20x²y
8x², – 11x², – 6x²
7y, y
– 100x, 3x
– 11yx, 2xy

(b) 10pq, 7p, 8q, – p2q2, – 7qp, – 100q, – 23, 12q2p2, – 5p2, 41, 2405p, 78qp,
Answer:
10pq, – 7qp, 78qp
7p, 2405p
8q, – 100q
– p²q², 12q²p²
– 23, 41
– 5p², 701p²
13p²q, qp²

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