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In class 6 Maths, we have studied algebraic expressions including simple calculations using variables like 𝑥 and 𝒚. We also learned to solve some real-life problems using these variables and algebraic expressions. Before proceeding to solve complex problems, we must note that the central idea of solving algebraic expressions is learning to express the given problem in the correct algebraic equation. Once you determine the algebraic equation correctly, you can use mathematical operations like addition, subtraction, multiplication, and division quite easily. Now, in NCERT Solutions of Class 7 Maths Chapter 10, we will learn to solve algebraic expressions involving squared variables. In this, we will learn to determine the factors and coefficients of a term in the given algebraic expression. Let us now have a look at the NCERT Class 7 Maths Chapter 10 Algebraic Expressions Notes and Solutions (PDF).
Download NCERT Class 7 Maths Chapter 10 – Algebraic Expressions Notes and Solutions PDF
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Download NCERT Class 7 Maths Chapter 10 – Algebraic Expressions Notes and Solutions PDF
NCERT Notes Class 7 Maths Chapter 10 – PDF Available
Check the topic-wise notes for NCERT Solutions Maths Class 7 Chapter 10, Algebraic Expressions below. You can also download the PDF of the notes and take a printout to study later when you need quick revision before going to the e𝑥am hall.
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Topic 1: Terms of an Expression
Such parts of an expression that are formed separately first and then added are known as terms.
For example, in the expression (4𝑥2 – 3𝑥y), 4𝑥2 and -3𝑥y are the terms of the given expression.
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Topic 2: Factors of a Term
A term is a product of its factors. In the above example, the factors of the term 4𝑥2 are 4, 𝑥 and 𝑥.
Topic 3: Coefficients
The numerical factor is said to be the numerical coefficient or simply the coefficient of the term. It is also said to be the coefficient of the rest of the term. In the above example, the coefficient of the term 4𝑥2 is 4 and of -3𝑥y is -3.
Topic 4: Monomials, Binomials, Trinomials and Polynomials
- Monomials: An expression with only one term is called a monomial; for example, 7𝑥y, – 5m, 3z2, 4 etc.
- Binomials: An expression that contains two unlike terms is called a binomial; for example, 𝑥 + y, m – 5, mn + 4m, a2 – b2 are binomials.
- Trinomials: An expression that contains three terms is called a trinomial; for example, the expressions 𝑥 + y + 7, ab + a +b, 3𝑥2 – 5𝑥 + 2, m + n + 10 are trinomials.
- Polynomials: In general, an expression with one or more terms is called a polynomial. Thus, a monomial, a binomial and a trinomial are all polynomials.
Download NCERT Class 7 Maths Chapter 10 – Algebraic Expressions Notes and Solutions PDF
Explore all the Chapters of Class Mathematics:-
| Chapter 1 | Chapter 2 | Chapter 3 | Chapter 4 | Chapter 5 |
| Chapter 6 | Chapter 7 | Chapter 8 | Chapter 9 | Chapter 10 |
| Chapter 11 | Chapter 12 | Chapter 13 |
NCERT Solutions of Class 7 Maths Chapter 10: Algebraic Expressions- PDF Available!
Below we have provided solutions for NCERT Solutions Class 7 Maths Chapter 10, Algebraic Expressions. Go through for answers to some important questions.
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E𝑥ercise 10.1 Solutions
Q 1. Get the algebraic expressions in the following cases using variables, constants, and arithmetic operations.
- Subtraction of z from y.
- The number z is multiplied by itself.
- One-fourth of the product of numbers p and q
- Number 5 is added to three times the product of numbers m and n.
Solutions. The answers are given below.
- y – z
- z2
- ¼(pq) = pq/4
- 3mn + 5
Q 2. Identify the numerical coefficients of terms (other than constants) in the following expressions:
- 5 – 3t2
- 1 + t + t2 + t3
- 0.1y + 0.01y2
- 1.2a + 0.8b
- -p2q2 + 7pq
Solutions. The answers are given below.
- In the given expression, 5 is a constant. So, in the term -3t2, the numerical coefficient is -3.
- In the given expression, 1 is a constant. So, in the terms t, t2 and t3, the numerical coefficients are 1, 1 and 1 respectively.
- The numerical coefficients of the terms 0.1y and 0.01y2 are 0.1 and 0.01 respectively.
- The numerical coefficients of the terms 1.2a and 0.8b are 1.2 and 0.8 respectively.
- The numerical coefficients of the terms -p2q2 and 7pq are -1 and 7 respectively.
Q 3. Classify into monomials, binomials and trinomials.
- 4y – 7z
- y2
- 𝑥 + y – 𝑥y
- z2 + z
- 1 + 𝑥 + 𝑥2
- z2 – 3z + 8
Solutions. The answers are given below.
- The given expression contains 2 terms, i.e. 4y and -7z. So it is a Binomial.
- The given expression contains only 1 term, i.e. y2. So, it is a Monomial.
- The given expression contains 3 terms, i.e. 𝑥, y and -𝑥y. So, it is a Trinomial.
- The given expression contains 2 terms, i.e. z2 and z. So, it is a Binomial.
- The given expression contains 3 terms, i.e. 1, 𝑥 and 𝑥2. So, it is a Trinomial.
- The given expression contains 3 terms, i.e. z2, -3z and 8. So, it is a Trinomial.
E𝑥ercise 10.2 Solutions
Q 1. If m = 2, find the value of:
- 3m2 – 2m – 7
- 9 – 5m
- 3m – 5
- m – 2
Solutions. Putting m = 2, the solutions of each of the given expressions can be determined. The solutions are given below.
- Given: 3m2 – 2m – 7
Putting m = 2 we get:
⇒ 3(2)2 – 2(2) – 7
⇒ 3 × 4 – 4 – 7 = 12 – 11 = 1
∴ the value of the given expression by putting m = 2 comes out to be 1.
- Given: 9 – 5m
Putting m = 2 we get:
⇒ 9 – 5(2)
⇒ 9 – 10 = -1
∴ the value of the given expression by putting m = 2 comes out to be -1.
- Given: 3m – 5
Putting m = 2 we get:
⇒ 3(2) – 5
⇒ 6 – 5 = 1
∴ the value of the given expression by putting m = 2 comes out to be 1.
- Given: m – 2
Putting m = 2 we get:
⇒ 2 -2
⇒ 0
∴ the value of the given expression by putting m = 2 comes out to be 0.
Q 2. If p = – 2, find the value of – 2p3 – 3p2 + 4p + 7.
Solutions: Given: – 2p3 – 3p2 + 4p + 7
Putting p = -2 we get:
⇒ – 2(-2)3 – 3(-2)2 + 4(-2) + 7
⇒ (-2 × -8) – (3 × 4) + (4 × -2) + 7
⇒ 16 – 12 – 8 + 7 = 3
∴ the value of the given expression by putting p = -2 comes out to be 3.
Q 3. Simplify the expressions and find the value if x is equal to 2.
- 𝑥 + 7 + 4 (𝑥 – 5)
- 4(2𝑥 – 1) + 3𝑥 + 11
Solutions: The solutions are given below.
- The given expression can be simplified by putting the terms with alike algebraic factors together. Hence, the given expression can be simplified as:
⇒ 𝑥 + 7 + (4 × 𝑥) – (4 × 5)
⇒ 𝑥 + 7 + 4𝑥 – 20
⇒ 5𝑥 -13
Now, putting 𝑥 = 2, we get:
⇒ 5(2) – 13
= 10 – 13 = -3
∴ the value of the given expression by putting 𝑥 = 2 comes out to be -3.
- The given expression can be simplified by putting the terms with alike algebraic factors together. Hence, the given expression can be simplified as:
⇒ (4 × 2𝑥) – (4 × 1) + 3𝑥 + 11
⇒ 8𝑥 – 4 + 3𝑥 + 11
⇒ 11𝑥 + 7
Now, putting 𝑥 = 2, we get:
⇒ 11(2) + 7
= 22 + 7 = 29
∴ the value of the given expression by putting 𝑥 = 2 comes out to be 29.
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FAQs
Ans: Such parts of an expression that are formed separately first and then added are known as terms.
For example, in the expression (4𝑥2 – 3𝑥y), 4𝑥2 and -3𝑥y are the terms of the given expression.
Ans: An algebraic expression with only one term is called a monomial; for example, 7𝑥y, – 5m, 3z2, 4 etc.
Ans: An expression with one or more terms is called a Polynomial. Thus, a monomial, a binomial and a trinomial are all polynomials.
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This was all about NCERT Solutions Class 7 Maths Chapter 10, Algebraic Expressions in which we studied the terms, factors and coefficients of Algebraic Expressions. Download the NCERT Solutions Class 7 Maths Chapter 10 Notes and Solutions PDF to ace your e𝑥am preparations. Follow the CBSE Class 7 Maths Solutions and Notes for more such chapter notes and important questions and answers for preparation for CBSE Class 7 Maths.