NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions

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NCERT Solutions for Class 7 Maths Chapter 12 Algebraic Expressions provides us with all-inclusive information on all concepts. As students would have to learn the basics about the subject in class 7, this curriculum for class 7 is comprehensive study material, which explains the concepts in a great way.

Questions Covered : 

Question 1 : Get the algebraic expressions in the following cases using variables, constants and arithmetic operations:
(i) Subtraction of z from y.
(ii) One half of the sum of numbers x and y.
(iii) The number z multiplied by itself.
(iv) One-fourth of the product of numbers p and q.
(v) Numbers x and y both squared and added.
(vi) Number 5 added to three times the product of number m and n.
(vii) Product of numbers y and 2 subtracted from 10.
(viii) Sum of numbers a and b subtracted from their product.

Question 2 : (i) Identify the terms and their factors in the following expressions show the terms and factors by tree diagrams.
(a) x – 3
(b) 1 + x + x2
(c) y – y3
(d) 5xy2 + 7x2y
(e) -ab + 2b2 – 3a2

Question 3 : Identify terms and factors in the expression
given below:
(a) -4x + 5
(b) -4x + 5y
(c) 5y + 3y2
(d) xy + 2x2y2
(e) pq + q
(f) 1.2ab – 2.4b + 3.6a
(g) 34x+14
(h) 0.1p2 + 0.2q2

Question 4 : Identify the numerical coefficients of terms (other than constants) in the following:
(i) 5 – 3t2
(ii) 1 + t + t2 + t3
(iv) 100m + 1000n
(v) -p2q2 + 7pq
(vi) 1.2 a + 0.86
(vii) 3.14r2
(viii) 2(l + b)
(ix) 0.1y + 0.01y2

Question 5 : (a) Identify terms which contain x and give the
coefficient of x.
(i) y2x + y
(ii) 13y2 – 8yx
(iii) x + y + 2
(iv) 5 + z + zx
(v) 1 + x + xy
(vi) 12 xy2 + 25
(vii) 7x + xy2

Question 6 : (b) Identify terms which contain y2 and give the coefficients of y2.
(i) 8 – xy2
(ii) 5y2 + 7x
(iii) 2x2y – 15xy2 + 7y2

Question 7 : Classify into monomials, binomials and trinomials.
(i) 4y – 7z
(ii) y2
(iii) x + y – xy
(iv) 100
(v) ab – a – b
(vi) 5 – 3t
(vii) 4p2q – 4pq2
(viii) 7mn
(ix) z2 – 3z + 8
(x) a2 + b2
(xi) z2 + z
(xii) 1 + x + x2

Question 8 : State whether a given pair of terms is of like or unlike terms.
(i) 1, 100
(ii) –7x, (5/2)x
(iii) – 29x, – 29y
(iv) 14xy, 42yx
(v) 4m2p, 4mp2
(vi) 12xz, 12x2z2

Question 9 : Identify like terms in the following:
(a) – xy2, – 4yx2, 8×2, 2xy2, 7y, – 11×2, – 100x, – 11yx, 20x2y, – 6×2, y, 2xy, 3x
(b) 10pq, 7p, 8q, – p2q2, – 7qp, – 100q, – 23, 12q2p2, – 5p2, 41, 2405p, 78qp,13p2q, qp2, 701p2

Question 10 : Simplify combining like terms:
(i) 21b – 32 + 7b – 20b
(ii) – z2 + 13z2 – 5z + 7z3 – 15z
(iii) p – (p – q) – q – (q – p)
(iv) 3a – 2b – ab – (a – b + ab) + 3ab + b – a
(v) 5x2y – 5×2 + 3yx2 – 3y2 + x2 – y2 + 8xy2 – 3y2
(vi) (3y2 + 5y – 4) – (8y – y2 – 4)

Question 11 : Add:
(i) 3mn, – 5mn, 8mn, – 4mn
(ii) t – 8tz, 3tz – z, z – t
(iii) – 7mn + 5, 12mn + 2, 9mn – 8, – 2mn – 3
(iv) a + b – 3, b – a + 3, a – b + 3
(v) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy
(vi) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5
(vii) 4x2y, – 3xy2, –5xy2, 5x2y
(viii) 3p2q2 – 4pq + 5, – 10 p2q2, 15 + 9pq + 7p2q2
(ix) ab – 4a, 4b – ab, 4a – 4b
(x) x2 – y2 – 1, y2 – 1 – x2, 1 – x2 – y2

Question 12 : Subtract:
(i) –5y2 from y2
(ii) 6xy from –12xy
(iii) (a – b) from (a + b)
(iv) a (b – 5) from b (5 – a)
(v) –m2 + 5mn from 4m2 – 3mn + 8
(vi) – x2 + 10x – 5 from 5x – 10
(vii) 5a2 – 7ab + 5b2 from 3ab – 2a2 – 2b2
(viii) 4pq – 5q2 – 3p2 from 5p2 + 3q2 – pq

Question 13 : (a) What should be added to x2 + xy + y2 to obtain 2×2 + 3xy?
(b) What should be subtracted from 2a + 8b + 10 to get – 3a + 7b + 16?

Question 14 : What should be taken away from 3×2 – 4y2 + 5xy + 20 to obtain – x2 – y2 + 6xy + 20?

Question 15 : (a) From the sum of 3x – y + 11 and – y – 11, subtract 3x – y – 11.
(b) From the sum of 4 + 3x and 5 – 4x + 2×2, subtract the sum of 3×2 – 5x and –x2 + 2x + 5.

Question 16 : If m = 2, find the value of:
(i) m – 2
(ii) 3m – 5
(iii) 9 – 5m
(iv) 3m2 – 2m – 7
(v) (5m/2) – 4

Question 17 : If p = – 2, find the value of:
(i) 4p + 7
(ii) – 3p2 + 4p + 7
(iii) – 2p3 – 3p2 + 4p + 7

Question 18 : Find the value of the following expressions, when x = –1:
(i) 2x – 7
(ii) – x + 2
(iii) x2 + 2x + 1
(iv) 2×2 – x – 2

Question 19 : If a = 2, b = – 2, find the value of:
(i) a2 + b2
(ii) a2 + ab + b2
(iii) a2 – b2

Question 20 : When a = 0, b = – 1, find the value of the given expressions:
(i) 2a + 2b
(ii) 2a2 + b2 + 1
(iii) 2a2b + 2ab2 + ab
(iv) a2 + ab + 2

Question 21 : Simplify the expressions and find the value if x is equal to 2
(i) x + 7 + 4 (x – 5)
(ii) 3 (x + 2) + 5x – 7
(iii) 6x + 5 (x – 2)
(iv) 4(2x – 1) + 3x + 11

Question 22 : Simplify these expressions and find their values if x = 3, a = – 1, b = – 2.
(i) 3x – 5 – x + 9
(ii) 2 – 8x + 4x + 4
(iii) 3a + 5 – 8a + 1
(iv) 10 – 3b – 4 – 5b
(v) 2a – 2b – 4 – 5 + a

Question 23 : (i) If z = 10, find the value of z3 – 3(z – 10)
(ii) If p = – 10, find the value of p2 – 2p – 100

Question 24 : What should be the value of a if the value of 2×2 + x – a equals to 5, when x = 0?

Question 25 : Simplify the expression and find its value when a = 5 and b = – 3.
2(a2 + ab) + 3 – ab

Question 26 : Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

Question 27 : Use the given algebraic expression to complete the table of number patterns.
S. No. Expression Terms
1st 2nd 3rd 4th 5th … 10th … 100th …
(i) 2n – 1 1 3 5 7 9 – 19 – – –
(ii) 3n + 2 5 8 11 14 – – – – – –
(iii) 4n + 1 5 9 13 17 – – – – – –
(iv) 7n + 20 27 34 41 48 – – – – – –
(v) n2 + 1 2 5 10 17 – – – – 10001 –