# Algebraic Expressions

## Exercise 12.1

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

1. Subtraction of z from y.

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

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

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

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

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

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

Answer: 10 – yz
8. 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.

1. x – 3

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

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

Answer: Term y and factor 1; term y^3 and factor – 1
4. 5xy^2 + 7x^2\y

Answer: Term xy2 and factor 5; term x2y and factor 7.
5. – 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:

1. – 4x + 5

Answer: Term x and factor – 4
2. – 4x + 5y

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

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

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

Answer: Term pq and factor 1; term q and factor 1.
6. 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.
7. 3/4x + 1/4

Answer: Term x and factor ¾ .
8. 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:

1. 5 – 3t^2

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

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

Answer: term x and coefficient 1, term xy and coefficient 2; term y and coefficient 3.
4. 100 m + 1000n

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

Answer: term p2q2 and coefficient – 1; term pq and coefficient 7.
6. 1.2 a + 0.8b

Answer: Term a and coefficient 1.2; term b and coefficient 0.8.
7. 3.14r^2

8. 2(l+b)

Answer: Term l and coefficient 2; term b and coefficient 2.
9. 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.

1. y^2 + y

2. 13y^2 – 8yx

3. x + y + 2

4. 5 + z + zx

5. 1 + x + xy

6. 12xy^2 + 25

7. 7x + xy^2

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

1. 8 – xy^2

2. 5y^2 + 7x

3. 2x^2\y – 15xy^2 + 7y^2

Question 7: Classify into monomials, binomials and trinomials.

1. 4y – 7z

2. y^2

3. x + y – xy

4. 100

5. ab – a – b

6. 5 – 3t

7. 4p^2\q – 4pq^2

8. 7mn

9. z^2 - 3z + 8

10. a^2 + b^2

11. z^2 + z

12. 1 + x + x^2

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

1. 1,  100

2. – 7x,  (5/2)x

3. – 29x,  - 29y

4. 14xy,  42yx

5. 4m^2p,  4mp^2

6. 12xz,  12x^2\z^2