RBSE Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.2

Rajasthan Board RBSE Solutions for Class 7 Maths Chapter 12 Algebraic Expressions Ex 12.2 Textbook Exercise Questions and Answers.

RBSE Class 7 Maths Solutions Chapter 12 Algebraic Expressions Ex 12.2

Question 1.
Simplify combining like terms :
(i) 21b - 32 + 7b - 20b
Answer:
21b - 32 + 7b - 20b
= (21b + 7b - 20b) - 32 (Combining like terms)
= (28b - 20b) - 32 = 8b - 32

(ii) - z² + 13z² -5z + 7z³ - 15²
Answer:
- z² + 13z² - 5z + 7z³ - 15z
= (- z² + 13z²) + (5z - 15z) + 7z³ (Combining like terms)
= 12z² - 20z + 7z³

(iii) p - (p - q) - q - (9 -p)
Answer:
p - (p - q) - q - (q - p)
= p - p + q - q - q + p (Combining like terms)
= (p - p + p) + (q - q - q) = P + (- q)
= p - q

(iv) 3a - 2b - ab - (a - b + ab) + 3ab + b - a
Answer:
3a - 2b - ab - (a - b + ab) + 3ab + b - a
= 3a - 2b - ab - a + b - ab + 3ab + b - a (Combining like terms)
= (3a - a - a) + (- 2b + b + b) + (-ab - ab + 3ab)
= (2a - a) + (- b + b) + (- 2ab + 3ab)
= a + 0 + ab = a + ab

(v) 5x²y - 5x² + 3yx² - 3y² + x² - y² + 8xy² - 3y²
Answer:
5x²y - 5x² + 3yx² - 3y² + x² - y² + 8xy² - 3y² = (5x²y + 3yx²) + (- 5x² + x²) + (- 3y² - y² - 3y²) + 8xy² (Combining like terms)
= 8x²y + (- 4x²) + (- 4y² - 3y²) + 8xy²
= 8x²y - 4x² - 7y² + 8xy²

(vi) (3y² + 5y - 4) - (8y - y² - 4)
Answer:
(3y² + 5y - 4) - (8y - y² - 4)
= 3y² + 5y - 4 - 8y + y² + 4 (Combining like terms)
= (3y² + y²) + (5y - 8y) + (- 4 + 4)
= 4y² - 3y + 0
= 4y² - 3y

Question 2.
Add: (i) 3mn, - 5mn, 8mn, - 4mn
Answer:
Sum = 3mn + (- 5mn) + 8mn + (- 4mn)
= (3mn - 5mn + 8mn - 4mn)
= (3mn + 8mn - 5mn - 4mn)
= 11mn - 9mn = 2 mn

(ii) t - 8tz, 3tz - z, z - t
Answer:
Sum = (t - 8tz) + (3tz - z) + (z - t)
= (t -1) + (- 8tz + 3tz) + (- 2 + 2)
= 0 - 5tz + 0 = - 5tz.

(iii) -7mn + 5, 12mn + 2, 9mn - 8, - 2mn - 3
Answer:
Sum = (- 7mn + 5) + (12mn + 2) + (9mn - 8) + (- 2mn - 3)
= (- 7mn + 12mn + 9mn - 2mn) + (5 + 2 - 8 - 3)
= (12mn + 9 mn - 7mn - 2mn) + (5 + 2 - 8 - 3)
= (21mn - 9mn) + (7 - 11)
= 12mn - 4

(iv) a + b - 3,b - a + 3, a - b + 3
Answer:
Sum = (a + b - 3) + (b - a + 3) + (a - b + 3)
= (a - a + a) + (b + b - b) + (- 3 + 3 + 3)
= (a + a - a) + (b + b - b) + (3 + 3 - 3)
= (2a - a) + (2b - b) + (b - 3)
= a + b + 3

(v) 14x + 10y - 12xy - 13, 18 - 7x - 10y + 8xy, 4xy
Answer:
Sum = (14x + 10y - 12xy - 13) + (18 - 7x - 10y + 8xy) + 4xy
= (14x- - 7x) + (10y - 10y) + (- 12xy + 8ay + 4xy) + (- 13 + 18)
= 7x + 0 + (- 12xy + 12xy) + (18 - 13)
= 7x + (12xy - 12xy) + 5
= 7x + 0 + 5
= 7x + 5

(vi) 5m - 7n, 3n - 4m + 2, 2m - 3mn - 5
Answer:
Sum = (5m - 7n) + (3n - 4m + 2) + (2m - 3mn - 5)
= (5m - 4m + 2m) + (- 7 n + 3 n) + (- 3 mn) + (2 - 5)
= (5m + 2m - 4m) + (-7n + 3n) + (-3mn) + (- 5 + 2)
= (7m - 4m) + (- 4n) - 3mn - 3
= 3m - 4n - 3mn - 3

(vii) 4x²y, - 3xy², - 5xy², 5x²y
Answer:
Sum = 4x²y + (- 3xy²) + (- 5xy²) + 5xzy
= (4x²y + 5x²y) + (- 3xy² - 5xy²)
= 9x²y + (- 8xy²)
= 9x²y - 8xy²

(viii) 3p²q² - 4pq + 5, - 10p²q², 15 + 9pq + 7p²q²
Answer:
Sum = (3p²q² - 4pq + 5) + (- 10p²q²) + (15 + 9pq + 7p²q²)
= (3p²q² - 10p²q² + 7p²q²) + (- 4pq + 9pq) + (5 + 15)
= (3p²q² + 7p²q² - 10p²g²) + (9pq - 4pq) + 20
= (10p²q² - 10p²q²) + 5pq + 20
= 0 + 5pq + 20 = 5pq + 20

(ix) ab - 4a, 4b - ab, 4a - 4b
Answer:
Sum = (ab - 4a) + (4b - ab) + (4a - 4b)
= (ab - ab) + (-4a + 4a) + (4b - 4b)
= 0 + 0 + 0 = 0

(x) x² - y² - 1, y² - 1 - x²,1 - x² - y²
Answer:
Sum = (x² - y² - 1) + (y² - 1 - x²) + (1 - x² - y²)
= (x² - x² - x²) + (-y² + y² - y²) + (- 1 - 1 + 1)
= (0 - x²) + (0 - y²) + (0 - 1)
= -x² - y² - 1

Question 3.
Subtract:
(i) - 5y² from y²
Answer:
Difference = y² - (- 5y²)
= y² + 5y²
= 6y²

(ii) 6xy from - 12xy
Answer:
Difference = - 12xy - (6xy)
= - 12xy - 6xy = - 18xy

(iii) (a - b) from (a + b)
Answer:
Difference = (a + b) - (a - b)
= a + b - a + b
= a - a + b + b
= 0 + b + b = 2b

(iv) a(b - 5) from 6(5 - a)
Answer:
Difference = b(5 - a) - a(b - 5)
= (5b - ab) - (ab - 5a)
= 5b - ab - ab + 5a
= (-ab - ab) + 56 + 5a
= - 2ab + 56 + 5a

(v) - m² + 5mn from 4m² - 3mn + 8
Answer:
Difference = (4m2 - 3mn + 8) - (- m² + 5 mn)
= 4m² - 3 mn + 8 + m² - 5 mn
= (4m² + m²) + (- 3mn - 5mn) + 8
= 5m² - 8mn + 8

(vi) - x² + 10x - 5 from 5x - 10
Answer:
Difference = (5x - 10) - (- x² + 10x - 5) = 5x - 10 + x² - 10x + 5
= (5x - 10x) + x² + (- 10 + 5)
= — 5x + x² — 5 = x² - 5x - 5

(vii) 5a² - 7ab + 5b² from 3ab - 2a² - 2b²
Answer:
Difference = (3ab - 2a² - 2b²)
- (5a² - 7ab + 5b²)
= 3ab - 2a² - 2b² - 5a² + 7ab - 5b² = (3ab + 7ab) + (- 2a² - 5a²) + (- 2b² - 5b²)
= 10ab - 7a² - 7b²
= - 7a² - 7b² + 10ab.

(viii) 4pq - 5q² - 3p² from 5p² + 3q² - pq
Answer:
Difference = (5p² + 3q² - pq)
- (4pq - 5q² - 3p²)
= 5p² + 3q² - pq - 4pq + 5 q² + 3p²
= (5p² + 3p²) + (3q² + 5q²) + (-pq - 4pq)
= 8p² + 8q² - 5pq.

Question 4.
(a) What should be added to x² + xy + y² to obtain zx² + 3xy?
Answer:
Required expression
= Difference of 2x² + 3x,y and x² + xy + y²
= (2x² + 3xy) - (x² + xy + y²)
= 2x² + 3xy - x² - xy - y²
= (2x² - x²) + (3xy -xy) - y² = x² + 2xy - y².

(b) What should be subtracted from 2a + 8b + 10 to get - 3a + 7b + 16?
Answer:
Required expression= Difference of 2a + 8b + 10 and - 3a + 7b + 16
= (2a + 8b + 10) - (- 3a + 7b + 16)
= 2a + 8b + 10 + 3a - 7b - 16
= (2a + 3a) + (8b - 7b) + (10 - 16)
= 5a + 6 + (- 6)
= 5a + 6 - 6

Question 5.
What should be taken away from 3x² - 4y² + 5xy + 20 to obtain - x² - y² + 6xy + 20?
Answer:
Required expression = Difference of 3x² - 4y² + 5xy + 20 and -x² - y² + 6xy + 20
= (3x² - 4y² + 5xy + 20) - (- x² - y² + 6xy + 20)
= 3x² - 4y² + 5xy + 20 + x² + y² - 6xy - 20
= (3x² + x² ) + (- 4y² + y² ) + (5xy - 6xy) + (20 - 20)
= 4x² - 3y² - xy + 0
= 4x² - 3y² - xy

Question 6.
(a) From the sum of 3x - y + 11 and - y - 11, subtract 3x - y - 11.
Answer:
Sum of 3x - y + 11 and -y - 11
= (3x - y + 11) + (-y - 11)
= 3x - y + 11 - y - 11
= 3x -y + 11 - y - 11
= 3x + (-y - y) + (11 - 11)
= 3x - 2y + 0 = 3x - 2y

Difference of 3x - 2y and 3a - y - 11
= (3x - 2y) - (3x - y - 11)
= 3x - 2y - 3x + y + 11
= (3x - 3x) + (- 2y + y) + 11
= 0 - y + 11
= - y + 11

(b) From the sum of 4 + 3x and 5 - 4x + 2x² , subtract the sum of 3x² - 5x and - x² + 2x + 5.
Answer:
Sum of 4 + 3x and 5 - 4x + 2x² = (4 + 3x) + (5 - 4x + 2x²)
= 4 + 3x + 5 - 4x + 2x²
= (4 + 5) + (3x - 4x) + 2x²
= 9 - x + 2x²
Sum of (3x² - 5x) and (- x² + 2x + 5)
= (3x² - 5x) + (- x² + 2x + 5)
= (3x² - x²) + (- 5x + 2x) + 5
= 2x² - 3x + 5

Now required expression = Difference of 9 - x + 2x² and 2x² - 3x + 5
= (9 - x + 2x²) - (2x² - 3x + 5)
= 9 - x + 2x² - 2x² + 3x - 5
= (2x² - 2x²) + (3x - x) + (9 - 5)
= 0 + 2x + 4 = 2x + 4