MP Board Class 7th Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1

MP Board Class 7th Maths Solutions 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.
(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 numbers m and n.
(vii) Product of numbers y and z subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.
Solution:
(i) y – z
(ii) \(\frac{1}{2}\)(x + y)
(iii) z2
(iv) \(\frac{1}{4}\)(pq)
(v) x2 + y2
(vi) 5 + 3 (mn)
(viii) 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
(b) 1 + x + x2
(c) y – y3
(d) 5xy2 + 7x2y
(e) -ab + 2b2 – 3a2

(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) 1.2ab – 2.4b + 3.6a
(g) \(\frac{3}{4}\)x + \(\frac{1}{4}\)
(h) 0.1p2 + 0.2q2
Solution:
(i)
MP Board Class 7th Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1 1
MP Board Class 7th Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1 2

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) 1.2a + 0.8b
(vii) 3.14 r2
(viii) 2(l + b)
(ix) 0.1y + 0.01y2
Solution:
MP Board Class 7th Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1 3
MP Board Class 7th Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1 4

MP Board Class 7th Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1

Question 4.
(a) Identify terms which contains 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 contains y2 and give the coefficient of y2.
(i) 8 – xy2
(ii) 5y2 + 7x
(iii) 2x2y – 15xy2 + 7y2
Solution:
(a)
MP Board Class 7th Maths Solutions Chapter 12 Algebraic Expressions Ex 12.1 5

Question 5.
Classify into 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
Solution:
The monomials, binomials and trinomials have 1, 2 and 3 unlike terms in it respectively.
(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

MP Board Solutions

Question 6.
State whether a given pair of terms is of like or unlike terms.
(i) 1,100
(ii) -7x, \(\frac{5}{2}\)x
(iii) -29x, -29y
(iv) 14xy, 42yx
(v) 4m2p, 4mp2
(vi) 12xz, 12x2z2
Solution:
The terms which have same algebraic factors are called like terms. However, when terms have different algebraic factors, these are called unlike terms.
(i) 1,100 Like
(ii) -7x, \(\frac{5}{2}\)x Like
(iii) -29x, -29y Unlike
(iv) 14xy, 42yx Like
(v) 4m2p, 4mp2 Unlike
(vi) 12xz, 12x2z2 Unlike

Question 7.
Identify like terms in the following:
(a) -xy2, -4yx2, 8x2, 2xy2, 7y, -11x2, -100x, -11yx, 20x2y, -6x2, y, 2xy, 3x
(b) 10pg, 7p, 8q, -p2q2, -7qp, – 100q, -23, 12q2p2, – 5p2, 41, 2405p, 78qp, 13p2g, qp2,701p2
Solution:
(a) -xy2 and 2xy2; -4yx2 and 20x2y; 8x2, -11x2 and -6x2; 7y and y, -100x and 3x; -11yx and 2xy

(b) 10pq, -7qp and 78qp; 7p and 2405p; 8q and -100y; -p2q2 and 12q2p2, -23 and 41; -5p2 and 701 p2; 13p22q and qp2

MP Board Class 7th Maths Solutions