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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 = Z^{2}

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

Solution:

v) Numbers x and y both squared and added.

Solution:

x^{2} + y^{2}

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 – y^{3}

Terms: y; -y^{3}

Factors : y ; -1, y,

d) 5xy^{2} + 7x^{2}y

Terms : 5xy^{2} ; 7x^{2}y

Factors : 5, x, y, y; 7, x, x, y

e) -ab + 2b^{2} – 3a^{2}

Terms : -ab ; 2b^{2}; 3a^{2}

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 + 3y^{2}

Terms : 5y ; 3y^{2}

Factors : 5, y ; 3, y, y

d) xy + 2x^{2}y^{2}

Terms : xy ; 2x^{2}y^{2}

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 p^{2} + 0.2 q^{2}

Terms : 0.1p^{2}; 0.2q^{2}

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 – 3t^{2}

Term other than constant = -3/2

numerical co-efficient = -3

ii) 1 + t + t^{2} + t^{3}

Term other than constant = t, t^{2}, t^{3}

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) -p^{2}q^{2} + 7pq

Terms other than constants = -p^{2} q^{2}, 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 r^{2}

Terms other than constants = 3.14r^{2}

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 y^{2}

Terms other than constants = 0.1 y, 0.01 y^{2}

Numerical co-efficients = 0.1, 0.01

Question 4.

a) Identify terms which contain x and give the coefficient of x.

i) y^{2}x + y

Terms which contains x — y^{2}

co-efficient of x — y^{2}

ii) 13y^{2} – 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) 12xy^{2} + 25 — 12xy^{2}

Terms which contains x

co-efficient of x — 12y^{2}

vii) 7x + xy^{2}

7x Terms which contains x

co-efficient of x —- 7

Terms which contains x — xy^{2}

y^{2} co-efficient of

b) Identify terms which contain y^{2} and give the coefficient of y’.

i) 8 – xy^{2}

Terms which contains y^{2}

xy^{2} co-efficient of y^{2} — x

ii) 5y^{2} + 7x

Terms which contains y^{2}

co-efficient of y^{2} — 5

iii) 2x^{2} y – 15xy^{2} + 7y^{2}

Terms which contains y^{2} — (-15xy^{2})

co-efficient of y^{2} — (-15x)

Terms which contain y^{2} — 7y^{2}

co-efficient of y^{2} —- 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) y^{2}

This is monomial expression because it contains only one term y^{2}.

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) 4p^{2}q – 4pq^{2}

This is binomial expression because it contains two terms 4p^{2}q and – 4 pq^{2}

viii) 7mn

This is monomial expression because it contains only one term 7mn.

ix) z^{2} – 3z + 8

This is trinomial expression because it contains three terms z^{2}, -3z and 8.

x) a^{2} + b^{2}

This is binomial expression because it contains two terms a^{2} and b^{2}.

xi) z^{2} + z

This is binomial expression because it contains 2 terms z^{2} and z.

xii) 1 + x + x^{2}

This is trinomial expression because it contains 3 terms 1, x and x^{2}.

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) 4m^{2}p, 4mp^{2}

unlike terms

vi) 12xz, 12x^{2}z^{2} unlike terms

Question 7.

Identify like terms in the following :

a) -xy^{2}, -4yx^{2}, 8x^{2}, 2xy^{2}, 7y, – 11x^{2}, 100x, – 11yx, 20x^{2}y, -6x^{2}, y, 2xy, 3x

Solutions:

Like terms are

i) -xy^{2}, 2xy^{2}

ii) -4yx^{2}, 20x^{2}y

iii) 8x^{2}, -11x^{2}, -6x^{2}

iv) 7y, y

v) -100x, 3x

vi) -11yx, 2xy

b) 10pq, 7p, 8q, -p^{2}q^{2}, -7qp, – 100q, -23, 12q^{2}p^{2}, -5p^{2}, 41, 2405p, 75qp, 13p^{2}q, qp^{2}, 701p^{2
}Solution:

like terms are

i) 10pq, – 7qp, 78qp,

ii) 7p, 2405p,

iii) 8q, -100q

iv) -23, 41,

v) 12q^{2}p^{2}, -p^{2}q^{2},

vi) -5p^{2}, 701p^{2},

vii) 13p^{2}q, qp^{2}