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

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1 Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1

Question 1.
Get the algebraic expressions in the following cases using variable, 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:
\(\frac{1}{2}\)(x + y)

(iii) The number * multiplied by itself.
Answer:
z²

(iv) One-fourth of the product of numbers p and q.
Answer:
\(\frac{1}{4}\)pq

(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 - yz

(viii) Sum of numbers a and b subtracted from their product.
Answer:
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:
Tree diagram:

(b) 1 + x + x²
Answer:
Tree diagram:

(c) y - y³
Answer:
Tree diagram:

(d) 5xy² + 7x²y
Answer:
Tree diagram:

(e) - ab + 2b² - 3a²
Answer:
Tree diagram:

(ii) Identify terms and factors in the expressions given below:
(a) - 4x + 5
Answer:
Expression : - 4x + 5
Terms: - 4x and 5
Factors : - 4, x and 5

(b) - 4x + 5y
Answer:
Expression: - 4x + 5y
Terms: - 4x and 5y
Factors : - 4, x and 5 ,y

(c) 5y + 3y²
Answer:
Expression : 5y + 3y²
Terms: 5y and 3y²
Factors : 5, y and 3, y, y

(d) xy + 2x²y²
Answer:
Expression : xy + 2x²y²
Terms: xy and 2x²y²
Factors: x, y and 2, x, x, y, y

(e) pq + q
Answer:
Expression: pq+q
Terms: pq and q
Factors : p, q and q

(f) 1.2ab - 2.4b + 3.6a
Answer:
Expression : 1.2 ab - 2.4b + 3.6a
Terms : 1.2ab and - 2.4b and 3.6a
Factors : 1.2, a, b and - 2.4, b and 3.6, a

(g) \(\frac{3}{4}\)x + \(\frac{1}{4}\)
Answer:
Expression : \(\frac{3}{4}\)x + \(\frac{1}{4}\)
Terms: \(\frac{3}{4}\) x and \(\frac{1}{4}\)
Factors: \(\frac{3}{4}\), x and \(\frac{1}{4}\)

(h) 0.1p² + 0.2q²
Answer:
Expression: 0.1p² + 0.2q²
Terms : 0.1p² and 0.2q²
Factors: 0.1, p, p and 0.2, q, q

Question 3.
Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 - 3t²
Answer:
Expression : 5 - 3t²
Terms (other than constants): - 3t²
Numerical coefficients : - 3

(ii) 1 + t + t² + t³
Answer:
Expression : 1 + t + t² + t³
Terms (other than constants): t, t² and t³
Numerical coefficients : 1,1 and 1

(iii) x + 2xy + 3y
Answer:
Expression : x + 2xy + 3y
Terms (other than constants): x, 2xy, 3y
Numerical coefficients : 1, 2 and 3

(iv) 100m + 1000n
Answer:
Expression : 100m + 1000n
Terms (other than constants): 100m and 1000n
Numerical coefficients : 100 and 1000

(v) -p²q² + 7pq
Answer:
Expression: -p²q² + 7pq
Terms (other than constants): -p²q² and 7pq
Numerical coefficients : - 1 and 7

(vi) 1.2a + 0.8b
Answer:
Expression : 1.2a + 0.8b
Terms (other than constants): 1.2a and 0.8b
Numerical coefficients : 1.2 and 0.8

(vii) 3.14r²
Answer:
Expression : 3.14r²
Terms (other than constants) : 3.14r²
Numerical coefficients : 3.14

(viii) 2(l + b)
Answer:
Expression : 2(l + b) or 21 + 2b
Terms (other than constants): 21 and 2b
Numerical coefficients : 2 and 2

(ix) 0.1y + 0.01y²
Answer:
Expression : 0.1y + 0.01y²
Terms (other than constants): 0.1y and 0.01y²
Numerical coefficients ; 0.1 and 0.01

Question 4.
(a) Identify terms which contain x and give the coefficient of x :
(i) y²x + y
Answer:
(i) Expression : y²x+y
Terms containing x : y²x
Coefficients of x: y²

(ii) 13y² - 8yx
Answer:
Expression: 13y² - 8yx
Terms containing x : -8yx
Coefficients of x : -8y

(iii) x + y + 2
Answer:
(iii) Expression: x + y + 2
Terms containing x: x
Coefficients of x : 1

(iv) 5 + z + zx
Answer:
Expression : 5 + z + zx
Terms containing x : zx
Coefficients of x: z

(v) 1 + x + xy
Answer:
Expression : 1 + x + xy
Terms containing x : x and xy
Coefficients of x in the term x : 1
Coefficients of x in the term xy : y

(vi) 12xy² + 25
Answer:
Expression : 12xy² + 25
Terms containing x: 12xy²
Coefficients of x : 12y²

(vii) 7x + xy²
Answer:
Expression: 7x + xy²
Terms containing x: 7x and xy²
Coefficients of x in the terms 7x: 7
Coefficients of x in the term xy²: y²

(b) Identify terms which contain y² and give the coefficient of y²:
(i) 8 - xy²
Answer:
Expression : 8 - xy²
Terms containing y² : - xy²
Coefficients of y² : - x

(ii) 5y² + 7x
Answer:
Expression : 5y² + 7x
Terms containing y² : 5y²
Coefficients of y² : 5

(iii) 2x²y - 15xy² + 7y²
Answer:
Expression : 2x²y - 15xy² + 7y²
Terms containing y² 15xy² and 7y²
Coefficients of y² in the term - 15xy² : -15x
Coefficients of y² in the term 7y² : 1

Question 5.
Classify into monomials, binomials and trinomials:
(i) 4y - 7z
Answer:
4y - 7z is a binomial as it contains two terms.

(ii) y²
Answer:
y² is a monomial as it contains only one term.

(iii) x + y - xy
Answer:
x + y - xy is a trinomial as it contains three terms.

(iv) 100
Answer:
100 is a monomial as it contains only one term.

(v) ab - a - b
Answer:
ab - a - b is a trinomial as it contains three terms.

(vi) 5 - 3t
Answer:
5 - 3t is a binomial as it contains two terms.

(vii) 4p²q - 4pq²
Answer:
4p²q - 4pq² is a binomial as it contains two terms.

(viii) 7mn
Answer:
7mn is a monomial as it contains only one term.

(ix) z² - 3z + 8
Answer:
z² - 3z + 8 is a trinomial as it contains three terms.

(x) a² + b²
Answer:
a² + b² is a binomial as it contains two terms.

(xi) z² + 3
Answer:
z² + 3 is a binomial as it contains two terms.

(xii) 1 + x + x²
Answer:
1 + x + x² is a trinomials as it contains three terms.

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

(ii) - 7x, \(\frac{5}{2}\)x
Answer:
-7x, \(\frac{5}{2}\)x are like terms as their algebraic factors are same.

(iii) - 29x, - 29y
Answer:
- 29x, - 29y are unlike terms as their algebraic factors are different.

(iv) 14xy, 42yx
Answer:
14xy, 42yx are like terms as their algebraic factors are same.

(v) 4m²p, 4mp²
Answer:
4m²p, 4mp² are.unlike terms as their algebraic factors are different.

(vi) 12xz,12x²z²
Answer:
12x2, 12x²z² are unlike terms as their algebraic factors are different.

Question 7.
Identify like terms in the following:
(a) - xy², - 4yx², 8x², 2xy², 7y, - 11x², - 100x, - 11yx, 20x²y, - 6x², y, 2xy, 3x.
Answer:
- xy² and 2xy² are the like terms; - 4yx² and 20x²y are like terms; 8x², - 11x² and - 6x² are like terms; - 11yx and 2xy are like terms; 7y and y are like terms; - 100x.and 3x are like terms.

(b) 10pq, 7p, 8q, - p²q², - 7qp, - 100q, - 23, 12q²p², - 5p², 41, 2405p, 78qp, 13p²q, qp², 701p².
Answer:
10pq, -7qp and 18qp are like terms; 7p and 2405p are like terms; 8q and - lOOg are like terms; - p²q² and 12q²p² are like terms; - 23 and 41 are like terms; - 5p² and 701p² are like terms; 13p²q and qp² are like terms.