KSEEB Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1

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Karnataka State Syllabus Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.1

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

1. Subtraction of z from y.
2. One-half of the sum of numbers x and y?
3. The number z multiplied by itself
4. One-fourth of the product of numbers p and q
5. Numbers x and y both squared and added.
6. Number 5 added to three times the product of numbers m and n.
7. Product of numbers and z subtracted from 10.
8. Sum of numbers a and b subtracted from their product.

Solution:

1. y – z
2. \(\frac{x+y}{2}\)
3. z × z = z²
4. \(\frac{p \times q}{4}=\frac{p q}{4}\)
5. x² + y²
   
6. mn + 5
7. 10 – yz
8. ab – (a + b)

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
Solution:
(a) x – 3

(b) 1 + x + x²

(c) y – y³

(d) 5xy² + 7x²y

(e) – ab + 2b² – 3a²

(ii) Identify terms and factors in the expressions given below:
(a) – 4x + 5
(b) – 4x + 5y
(c) 5y + 3y²
(d) xy + 2x²y²
(e) pq + q
(f) 1.2 ab – 2.4 b + 3.6 a
(g) \(\frac{3}{4}\) x + \(\frac{1}{4}\)
(h) 0.1p² + 0.2q²
Solution:

Question 3.
Identify the numerical coefficients of terms (other than constants) in the following expressions:
(i) 5 – 3t²
(ii) 1 + t + t² + t³
(iii) x + 2xy + 3y
(iv) 100m + 1000n
(v) – p²q² + 7pq
(vi) 1.2 a + 0.8 b
(vii) 3.14 r²
(viii) 2 (l + b)
(ix) 0.1 y + 0.01y²
Solution:

Question 4.
(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) 12xy² + 25
(vii) 7x + xy²
Solution:

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

Question 5.
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
Solution:

Question 6.
State whether a given pair of terms is of like or unlike terms.

1. 1,100
2. -7x, \(\frac{5}{2}\)x
3. -29x, -29y
4. 14xy, 42yx
5. 4m²p, 4mp²
6. 12xz, 12x²z²

Solution:

1. Like
2. Like
3. Unlike
4. Like
5. Unlike
6. Unlike

Question 7.
Identify like terms in the following:
(a) – xy², – 4yx², 8x², 2xy², 7y, – 11x², – 100x, 11yx, 20x²y, – 6x², y, 2xy, 3x
Solution:
– xy², 2xy², – 4yx², 20x²y; 8x², – 6x², – 11x², 7y, y, – 100x, 3x, – 11yx, 2xy

(b) 10pq, 7p, 8q, – p²q², – 7qp, – 100q, – 23, 12q²p², – 5p², 41, 2405p, 78qp, 13p²q, qp², 701p²
Solution:
10pq, – 7pq, 78qp, 7p, 2405p, 8q, – 100q, – p²q², – 23, 41, – 5p² , 701p², 13p²q, qp²