This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Like and Unlike Terms, Addition and Subtraction of Algebraic Expressions”.

1. Identify the like terms: 3ab – 4b^{2} – 6ab.

a) 3ab, -6ab

b) -4b^{2}, 3ab

c) 3ab, 6ab

d) -4b^{2}, 6ab

View Answer

Explanation: An algebraic expression is combination of terms with algebraic operations like addition, subtraction, multiplication. The terms having same literal factors are called like terms. Like terms are formed from same variables and the powers of the variables are similar. But, coefficients of the like terms can be different. Eg: 2x, 3x form a pair of like terms; 5ax, -ax form a pair of like terms.

2. Identify the like terms: 4xy – 3y + 44y.

a) -3y, 44y

b) 4xy, 44y

c) 44y, -3y

d) 3y, 44y

View Answer

Explanation: An algebraic expression is combination of terms with algebraic operations like addition, subtraction, multiplication. The terms having same literal factors are called like terms. Like terms are formed from same variables and the powers of the variables are similar. But, coefficients of the like terms can be different. Eg: 2x, 3x form a pair of like terms; 5ax, -ax form a pair of like terms.

3. Identify all the unlike terms: 2a – 3b – 4c.

a) 2a, 4c

b) 2a, 3b, 4c

c) 2a, -3b, 4c

d) 2a, -3b, -4c

View Answer

Explanation: An algebraic expression is combination of terms with algebraic operations like addition, subtraction, multiplication. The terms which are not having same literal factors are called unlike terms. Unlike terms have different variables and the powers of the variables can be different. But, coefficients of the like terms can be different. Eg: 3x, 4yx form a pair of like terms; 5ax, -ax form a pair of like terms.

4. Identify the unlike terms: 3a^{2}b + 4b^{2}a – ba^{2}.

a) 3a^{2}b, 4b^{2}a

b) 3a^{2}b, -ba^{2}

c) 3a^{2}b, ba^{2}

d) 4b^{2}a, -ba^{2}

View Answer

Explanation: An algebraic expression is combination of terms with algebraic operations like addition, subtraction, multiplication. The terms which are not having same literal factors are called unlike terms. Unlike terms have different variables and the powers of the variables can be different. But, coefficients of the like terms can be different. Eg: 3x, 4yx form a pair of like terms; 5ax, -ax form a pair of like terms.

5. What will be the result if the expressions 2x – 4x^{2}y and 16y^{2}x + 2x^{2}y are added?

a) 2x – 4x^{2}y + 18x^{2}y

b) 2x – 2x^{2}y + 16y^{2}x

c) 2x – 2x^{2}y – 16y^{2}x

d) 2x + 4x^{2}y + 18x^{2}y

View Answer

Explanation: The terms of an algebraic expression having same literal factors are called like terms and those terms with different literal factors are called unlike terms. While addition or subtraction of polynomials, like terms are added/subtracted first and then unlike terms are handled. In the given expressions, -4x

^{2}y and 2x

^{2}y are like terms.

⇒ (2x – 4x

^{2}y) + (16y

^{2}x + 2x

^{2}y) = 2x – 4x

^{2}y + 2x

^{2}y + 16y

^{2}x (Collecting like terms)

⇒ (2x – 4x

^{2}y) + (16y

^{2}x + 2x

^{2}y) = 2x – 2 x

^{2}y + 16y

^{2}x (Adding like terms).

6. Find the value the following expression: 1/6x + 2/5xy – 13y – 7/5xy + 1/6x.

a) 2/3x – 9/5xy – 13y

b) 2/3x + 1xy – 13y

c) 2/3x – 1xy – 13y

d) -1xy – 13y

View Answer

Explanation: 1/6x + 2/5xy – 13y – 7/5xy + 1/6x = 1/6x + 1/6x + 2/5xy – 7/5xy – 13y (Collecting like terms)

= 2/3x – 1xy – 13y (Adding like terms).

7. Subtract the following expression: 22ab – 30a^{2}b + 2b from 50a^{2}b – 6b^{2}a – 5b.

a) 22ab – 80a^{2}b – 6b^{2} – 7b

b) 80a^{2}b – 6b^{2} + 7b – 22ab

c) 80a^{2}b – 6b^{2} – 7b – 22ab

d) 80a^{2}b + 6b^{2} – 7b

View Answer

Explanation: (50a

^{2}b – 6b

^{2}a – 5b) – (22ab – 30a

^{2}b + 2b) = 50a

^{2}b – 6b

^{2}a – 5b – 22ab + 30a

^{2}b + 2b

= 50a

^{2}b + 30a

^{2}b – 6b

^{2}– 5b – 2b (Collecting like terms)

= 80a

^{2}b – 6b

^{2}– 7b22ab (Adding/subtracting like terms).

**Sanfoundry Global Education & Learning Series – Mathematics – Class 8**.

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