In Chapter 10 of Class 7 Maths, you’ll learn about algebraic expressions. You’ve already seen simple ones like x + 3 or 4x + 5 in class 6. Algebraic expressions mix numbers and letters to describe math problems. You use letters like x or y for variables. You use operations like adding, subtracting, multiplying, or dividing to combine these with fixed numbers, called constants.
When you multiply a variable by itself, like x times x, you write it as x squared, or x². If you multiply it three times, like x times x times x, it’s x cubed or x³. You can also mix different variables together, like x times y to get xy.
In expressions, each piece that you add together is called a term. For example, in 4x + 5, the 4x is one term, and the 5 is another term. The number in front of the letter, like the 4 in 4x, is called the coefficient. It tells you how many of that variable you have. If there’s a 1 in front, we usually skip writing it. If there’s a -1, we just write a minus sign.
So, this chapter is all about learning to put together and understand these algebraic expressions and their parts.
NCERT Question and Answers for Class 7 Maths Exercise 10.1 Chapter 10 Algebraic Expressions
Question 1: Get the algebraic expressions in the following cases using variables, constants, and arithmetic operations.
(i) Subtraction of z from y
y – z
(ii) One-half of the sum of numbers x and y
1/2 * (x + y)
(iii) The number z multiplied by itself
z * z or z²
(iv) One-fourth of the product of numbers p and q
1/4 * (p * q)
(v) Numbers x and y both squared and added
x² + y²
(vi) Number 5 added to three times the product of numbers m and n
5 + 3 * (m * n)
(vii) Product of numbers y and z subtracted from 10
10 – (y * z)
(viii) Sum of numbers a and b subtracted from their product
(a * b) – (a + b)
Question 2:
(i) Identify the terms and their factors in the following expressions:
(a) x – 3
Terms are x and -3
Factors of x are x, factors of -3 are -3.
(b) 1 + x + x²
Terms are 1, x, and x²
Factors are 1, x, x * x.
(c) y – y³
Terms are y and -y³
Factors are y, y * y * y.
(d) 5xy² + 7x²y
Terms are 5xy² and 7x²y
Factors are 5, x, y, y and 7, x, x, y.
(e) -ab + 2b² – 3a²
Terms are -ab, 2b², -3a²
Factors are -1, a, b, 2, b, b, -3, a, a.
(ii) Identify terms and factors in the expressions given below:
(a) -4x + 5
Terms are -4x and 5
Factors are -4, x and 5.
(b) -4x + 5y
Terms are -4x and 5y
Factors are -4, x and 5, y.
(c) 5y + 3y²
Terms are 5y and 3y²
Factors are 5, y and 3, y, y.
(d) xy + 2x²y²
Terms are xy and 2x²y²
Factors are x, y and 2, x, x, y, y.
(e) pq + q
Terms are pq and q
Factors are p, q and q.
(f) 1.2 ab – 2.4 b + 3.6 a
Terms are 1.2 ab, -2.4 b, 3.6 a
Factors are 1.2, a, b, -2.4, b, 3.6, a.
(g) 3/4 x + 1/4
Terms are 3/4 x and 1/4
Factors are 3/4, x and 1/4.
(h) 0.1 p² + 0.2 q²
Terms are 0.1 p² and 0.2 q²
Factors are 0.1, p, p and 0.2, q, q.
Question 3: Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 – 3t²
Coefficient of -3t² is -3.
(ii) 1 + t + t² + t³
Coefficients are 1 for t, 1 for t², and 1 for t³.
(iii) x + 2xy + 3y
Coefficients are 1 for x, 2 for 2xy.
(iv) 100m + 1000n
Coefficients are 100 for 100m, 1000 for 1000n.
(v) -p²q² + 7pq
Coefficients are -1 for -p²q², 7 for 7pq.
(vi) 1.2a + 0.8b
Coefficients are 1.2 for 1.2a, 0.8 for 0.8b.
(vii) 3.14 r²
Coefficient of 3.14 r² is 3.14.
(viii) 2 (l + b)
Coefficients are 2 for 2l and 2 for 2b.
(ix) 0.1 y + 0.01 y²
Coefficients are 0.1 for 0.1 y and 0.01 for 0.01 y²
Question 4:
(a) Identify terms which contain x and give the coefficient of x.
(i) y²x + y
Contains y²x
Coefficient of x is y².
(ii) 13y² – 8yx
Contains -8yx
Coefficient of x is -8y.
(iii) x + y + 2
Contains x
Coefficient of x is 1.
(iv) 5 + z + zx
Contains zx
Coefficient of x is z.
(v) 1 + x + xy
Contains x and xy
Coefficients of x are 1 and y.
(vi) 12xy² + 25
Contains 12xy²
Coefficient of x is 12y².
(vii) 7x + xy²
Contains 7x and xy²
Coefficients of x are 7 and y².
(b) Identify terms which contain y² and give the coefficient of y².
(i) 8 – xy²
Contains -xy²
Coefficient of y² is -x.
(ii) 5y² + 7x
Contains 5y²
Coefficient of y² is 5.
(iii) 2x²y – 15xy² + 7y²
Contains -15xy² and 7y²
Coefficients of y² are -15x and 7.
Question 5: Classify into monomials, binomials, and trinomials.
(i) 4y – 7z:
Expression is Binomial as it contains 2 terms: 4y and 7z
(ii) y²: Monomial
Expression is Monomial as it contains 1 term: y²
(iii) x + y – xy: Trinomial
Expression is Trinomial as it contains 3 terms: x, y and -xy
(iv) 100: Monomial
Expression is Monomial as it contains 1 term: 100
(v) ab – a – b: Trinomial
Expression is Trinomial as it contains 3 terms: ab, -a and -b
(vi) 5 – 3t: Binomial
Expression is Binomial as it contains 2 terms: 5 and -3
(vii) 4p²q – 4pq²: Binomial
Expression is Binomial as it contains 2 terms: 4p²q and –4pq²
(viii) 7mn: Monomial
Expression is Monomial as it contains 1 term: 7mn
(ix) z² – 3z + 8: Trinomial
Expression is Trinomial as it contains 3 terms: z², -3z and 8
(x) a² + b²: Binomial
Expression is Binomial as it contains 2 terms: a² and b²
(xi) z² + z: Binomial
Expression is Binomial as it contains 2 terms: z² and z
(xii) 1 + x + x²: Trinomial
Expression is Trinomial as it contains 3 terms: 1, x and x²
Question 6: State whether a given pair of terms is of like or unlike terms.
(i) 1, 100
Like terms (both are constants)
(ii) –7x, 5/2 x
Like terms (both have the variable x)
(iii) – 29x, – 29y
Unlike terms (different variables x and y)
(iv) 14xy, 42yx
Like terms (same variables x and y)
(v) 4m²p, 4mp²
Unlike terms (different variable powers)
(vi) 12xz, 12x²z²
Unlike terms (different variable powers)
Question 7: Identify like terms in the following:
(a) – xy², – 4yx², 8x², 2xy², 7y, – 11x², – 100x, – 11yx, 20x²y, – 6x², y, 2xy, 3x:
Like terms: -xy² and 2xy²
Like terms: -4yx², 8x², -11x², and -6x²
Like terms: 7y and y
Like terms: -100x and 3x
(b) 10pq, 7p, 8q, – p²q², – 7qp, – 100q, – 23, 12q²p², – 5p², 41, 2405p, 78qp, 13p²q, qp², 701p²:
Like terms: 10pq and -7qp
Like terms: 7p and 2405p
Like terms: 8q and -100q
Like terms: -p²q² and 12q²p²
Like terms: -5p² and 701p²
