Class 7 Maths

Algebraic Expressions

Exercise 12.1

Question 1: Get the algebraic expression in the following cases using variables, constants and arithmetic operations.

• Subtraction of z from y.

Answer: y – z
• One half of the sum of numbers x and y.

Answer: (x + y) ÷ 2
• The number z multiplied by itself.

Answer: z^2
• One fourth of the product of numbers p and q.

Answer: (p × q) ÷ 4
• Numbers x and y both squared and added.

Answer: x^2 + y^2
• Number 5 added to three times the product of numbers m and n.

Answer: 3mn + 5
• Product of numbers y and z subtracted from 10.

Answer: 10 – yz
• Sum of numbers a and b subtracted from their product.

Answer: ab – (a + b)

Question 2: Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.

• x – 3

Answer: term = x and factor = 1
• 1 + x + x^2

Answer: Term x and factor 1; term x^2 and factor 1
• y – y^3

Answer: Term y and factor 1; term y^3 and factor – 1
• 5xy^2 + 7x^2\y

Answer: Term xy2 and factor 5; term x2y and factor 7.
• – ab + 2b^2 – 3a^2

Answer: Term ab and factor – 1; term b2 and factor 2; term a2 and factor – 3

Question 3: Identify terms and factors in the expression given below:

• – 4x + 5

Answer: Term x and factor – 4
• – 4x + 5y

Answer: Term x and factor – 4; term y and factor 5.
• 6y + 3y^2

Answer: Term y and factor 6; term y2 and factor 3.
• xy + 2x^2\y^2

Answer: Term xy and factor 1; term x2y2 and factor 2.
• pq + q

Answer: Term pq and factor 1; term q and factor 1.
• 1.2 ab – 2.4 b + 3.6 a

Answer: Term ab and factor 1.2; term b and factor 2.4; term a and factor 3.6.
• 3/4x + 1/4

Answer: Term x and factor ¾ .
• 0.1p^2 + 0.2q^2

Answer: Term p2 and factor 0.1; term q2 and factor 0.2

Question 4: Identify the numerical coefficients of terms (other than constants) in the following expressions:

• 5 – 3t^2

Answer: Term t2 and coefficient – 3.
• 1 + t + t^2 + t^3

Answer: Term t and coefficient 1; term t2 and coefficient 1; term t3 and coefficient 1.
• x + 2xy + 3y

Answer: term x and coefficient 1, term xy and coefficient 2; term y and coefficient 3.
• 100 m + 1000n

Answer: term m and coefficient 100; term n and coefficient 1000.
• – p^2\q^2 + 7pq

Answer: term p2q2 and coefficient – 1; term pq and coefficient 7.
• 1.2 a + 0.8b

Answer: Term a and coefficient 1.2; term b and coefficient 0.8.
• 3.14r^2

• 2(l+b)

Answer: Term l and coefficient 2; term b and coefficient 2.
• 0.1y + 0.01y^2

Answer: Term y and coefficient 0.1; term y2 and coefficient 0.01.

Question 5: Identify terms which contain x and give the coefficient of x.

• y^2 + y

• 13y^2 – 8yx

• x + y + 2

• 5 + z + zx

• 1 + x + xy

• 12xy^2 + 25

• 7x + xy^2

Question 6: Identify the terms which contain y2 and give the coefficient of y2.

• 8 – xy^2

• 5y^2 + 7x

• 2x^2\y – 15xy^2 + 7y^2

Question 7: Classify into monomials, binomials and trinomials.

• 4y – 7z

• y^2

• x + y – xy

• 100

• ab – a – b

• 5 – 3t

• 4p^2\q – 4pq^2

• 7mn

• z^2 - 3z + 8

• a^2 + b^2

• z^2 + z

• 1 + x + x^2

Question 8: State whether a given pair of terms is of like or unlike terms.

• 1,  100

• – 7x,  (5/2)x

• – 29x,  - 29y

• 14xy,  42yx

• 4m^2p,  4mp^2

• 12xz,  12x^2\z^2