KSEEB Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1

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Karnataka State Syllabus Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1

Question 1.
Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
i) Subtraction of z from y.
Solution:
y – z

ii) One-half of the sum of numbers x and
Solution:

iii) The number z multiplied by itself.
Solution:
Z × Z = Z²

iv) One- fourth of the product of numbers p and q.
Solution:

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

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

vii) Product of numbers y and z subtracted from 10.
Solution:
10 – yz

viii) Sum of numbers a and b subtracted from their product.
Solution:
ab, – {a + b)

Question 2.
i) Identify the terms and their factors in the following expression show the terms and factors by tree diagrams.
Solution:

c) y – y³
Terms: y; -y³

Factors : y ; -1, y,

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

e) -ab + 2b² – 3a²
Terms : -ab ; 2b²; 3a²
Factors : 1, a, b ; 2, b, b ; -3, a, a

ii) Identify terms and factors in the expressions given below :

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

b) -4x + 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) 1.2 ab – 2.4b + 3.6a
Terms : 1.2 ab ; 2.4b ; 3.6a
Factors : 1.2, a, b ; -2.4, b ; 3.6, a

g)

Solution:

h) 0.1 p² + 0.2 q²
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
Term other than constant = -3/2
numerical co-efficient = -3

ii) 1 + t + t² + t³
Term other than constant = t, t², t³
Numerical co-efficients = 1, 1, 1.

iii) x + 2xy + 3y
Terms other than constants = x, 2xy + 3y
Numerical co-efficients = 1, 2, 3

iv) 100m + 1000n
Terms other than constants = 100m, 1000n
Numerical co-efficients = 100, 1000.

v) -p²q² + 7pq
Terms other than constants = -p² q², 7 pq
Numerical co-efficients = -1, 7

vi) 1.2a + 0.8b
Terms other than constants = 1.2a, 0.8b
Numerical co-efficients = 1.2, 0.8

vii) 3.14 r²
Terms other than constants = 3.14r²
Numerical co-efficients = 3.14

viii) 2 (l + b)
Terms other than constants = 2l, 2b
(∵ 2(l + b) = 2l + 2b)
Numerical co-efficients = 2, 2

ix) 0.1 y + 0.01 y²
Terms other than constants = 0.1 y, 0.01 y²
Numerical co-efficients = 0.1, 0.01

Question 4.
a) Identify terms which contain x and give the coefficient of x.
i) y²x + y
Terms which contains x — y²
co-efficient of x — y²

ii) 13y² – 8yx
Terms which contains x — (x – 8yx)
co-efficient of x — (-8y)

iii) x + y + 2
Terms which contains x —- x
co-efficient of x —- 1

iv) 5 + z + zx
Terms which contains x — x
co-efficient of x — z

v) 1 + x + xy
Terms which contains x — x and xy
co-efficient of x — 1 y

vi) 12xy² + 25 — 12xy²
Terms which contains x
co-efficient of x — 12y²

vii) 7x + xy²
7x Terms which contains x
co-efficient of x —- 7
Terms which contains x — xy²
y² co-efficient of

b) Identify terms which contain y² and give the coefficient of y’.
i) 8 – xy²
Terms which contains y²
xy² co-efficient of y² — x

ii) 5y² + 7x
Terms which contains y²
co-efficient of y² — 5

iii) 2x² y – 15xy² + 7y²
Terms which contains y² — (-15xy²)
co-efficient of y² — (-15x)
Terms which contain y² — 7y²
co-efficient of y² —- 7

Question 5.
Classify into monomials, binomials and trinomials.
i) 4y – 7z
This expression is binomial because it contains two terms. That is 4 y and -7z.
ii) y²
This is monomial expression because it contains only one term y².
iii) x + y – xy
This is trinomial expression because it contains three terms x, y and -xy.
iv) 100
This is a monomial expression because it contains only one term 100.
v) ab – a – b
This is trinomial expression because it contains 3 terms ab, -a and -b.
vi) 5 – 3t
This is binomial expression because it contains 2 terms 5 and -3t.
vii) 4p²q – 4pq²
This is binomial expression because it contains two terms 4p²q and – 4 pq²
viii) 7mn
This is monomial expression because it contains only one term 7mn.
ix) z² – 3z + 8
This is trinomial expression because it contains three terms z², -3z and 8.
x) a² + b²
This is binomial expression because it contains two terms a² and b².
xi) z² + z
This is binomial expression because it contains 2 terms z² and z.
xii) 1 + x + x²
This is trinomial expression because it contains 3 terms 1, x and x².

Question 6.
State whether a given pair of terms is of like or unlike terms.
i) 1, 100
like terms
ii)
like terms
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
Solutions:
Like terms are
i) -xy², 2xy²
ii) -4yx², 20x²y
iii) 8x², -11x², -6x²
iv) 7y, y
v) -100x, 3x
vi) -11yx, 2xy

b) 10pq, 7p, 8q, -p²q², -7qp, – 100q, -23, 12q²p², -5p², 41, 2405p, 75qp, 13p²q, qp², 701p²
Solution:
like terms are
i) 10pq, – 7qp, 78qp,
ii) 7p, 2405p,
iii) 8q, -100q
iv) -23, 41,
v) 12q²p², -p²q²,
vi) -5p², 701p²,
vii) 13p²q, qp²