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## Chapter 12 Algebraic Expressions Exercise 12.2

Question 1: Simplify combining like terms:
(i) 21b - 32 + 7b - 20b

= 21b - 32 + 7b - 20
= 21b - 20b + 7b - 32
= 1b + 7b - 32
= 8b - 32

(ii) -z² + 13z² - 5z + 7z³ - 15z

= -z² + 13z² - 5z + 7z³ - 15z
= 7z³ + (-z² + 13z²) + (-5z - 15z)
= 7z³ + -z² + 13z² + -5z - 15z
= 7z³ + 12z² + -20z
= 7z³ + 12z² - 20z

(iii) p - (p - q) - q - (q - p)

= p - (p - q) - q - (q - p)
= p - p + q - q - q + p
= p - q

(iv) 3a - 2b - ab - (a - b + ab) + 3ab + b - a

= 3a - 2b - ab - (a - b + ab) + 3ab + b - a
= 3a - 2b - ab - a + b - ab + 3ab + b - a
= 3a - a - a - 2b + b + b - ab - ab + 3ab
= a + ab

(v) 5x²y - 5x² + 3yx² - 3y² + x² - y² + 8xy² - 3y²

= 5x²y - 5x² + 3yx² - 3y² + x² - y² + 8xy² - 3y²
= 5x²y + 3yx² - 5x² + x² - 3y² - y² - 3y² + 8xy²
= 8x²y - 4x² - 7y² + 8xy²

(vi) (3y² + 5y - 4) - (8y - y² - 4)

= (3y² + 5y - 4) - (8y - y² - 4)
= 3y² + 5y - 4 - 8y + y² + 4
= 3y² + y² + 5y - 8y - 4 + 4
= 4y² - 3y

(i) 3mn, - 5mn, 8mn, - 4mn

= 3mn + (-5mn) + 8mn + (-4mn)
= 3mn - 5mn + 8mn - 4mn
= 3mn + 8mn - 5mn - 4mn
= 11mn - 9mn
= 2mn

(ii) t - 8tz, 3tz - z, z - t

= t - 8tz + (3tz - z) + (z - t)
= t - 8tz + 3tz - z + z - t
= t - t - 8tz + 3tz - z + z
= - 5tz

(iii) - 7mn + 5, 12mn + 2, 9mn - 8, - 2mn - 3

= - 7mn + 5 + 12mn + 2 + (9mn - 8) + (- 2mn - 3)
= - 7mn + 5 + 12mn + 2 + 9mn - 8 - 2mn - 3
= - 7mn + 12mn + 9mn - 2mn + 5 + 2 - 8 - 3
= 12mn - 4

(iv) a + b - 3, b - a + 3, a - b + 3

= a + b - 3 + (b - a + 3) + (a - b + 3)
= a + b - 3 + b - a + 3 + a - b + 3
= a - a + a + b + b - b - 3 + 3 + 3
= a + b + 3

(v) 14x + 10y - 12xy - 13, 18 - 7x - 10y + 8xy, 4xy

= 14x + 10y - 12xy - 13 + (18 - 7x - 10y + 8xy) + 4xy
= 14x + 10y - 12xy - 13 + 18 - 7x - 10y + 8xy + 4xy
= 14x - 7x + 10y - 10y - 12xy + 8xy + 4xy - 13 + 18
= 7x + 5

(vi) 5m - 7n, 3n - 4m + 2, 2m - 3mn - 5

= 5m - 7n + (3n - 4m + 2) + (2m - 3mn - 5)
= 5m - 7n + 3n - 4m + 2 + 2m - 3mn - 5
= 5m - 4m + 2m - 7n + 3n - 3mn + 2 - 5
= 3m - 4n - 3mn - 3

(vii) 4x²y, - 3xy², - 5xy², 5x²y

= 4x²y + (-3xy²) + (-5xy²) + 5x²y
= 4x²y + 5x²y - 3xy² - 5xy²
= 9x²y - 8xy²

(viii) 3p²q² - 4pq + 5, - 10 p²q², 15 + 9pq + 7p²q²

= 3p²q² - 4pq + 5 + (-10p²q²) + 15 + 9pq + 7p²q²
= 3p²q² - 10p²q² + 7p²q² - 4pq + 9pq + 5 + 15
= 5pq + 20

(ix) ab - 4a, 4b - ab, 4a - 4b

= ab - 4a + (4b - ab) + (4a - 4b)
= ab - 4a + 4b - ab + 4a - 4b
= ab - ab - 4a + 4a + 4b - 4b
= 0

(x) x² - y² - 1, y² - 1 - x², 1 - x² - y²

= x² - y² - 1 + (y² - 1 - x²) + (1 - x² - y²)
= x² - y² - 1 + y² - 1 - x² + 1 - x² - y²
= x² - x² - x² - y² + y² - y² - 1 - 1 + 1
= -x² - y² -1

Question 3: Subtract:
(i) -5y
² from y²

= y² - (-5y²)
= y² + 5y²
= 6y²

(ii) 6xy from -12xy

= -12xy - 6xy
= -18xy

(iii) (a - b) from (a + b)

= (a + b) - (a - b)
= a + b - a + b
= a - a + b + b
= 2b

(iv) a (b - 5) from b (5 - a)

= b (5 - a) - a (b -5)
= 5b - ab - ab + 5a
= 5b + ab (-1 - 1) + 5a
= 5a + 5b - 2ab

(v) -m² + 5mn from 4m² - 3mn + 8

= 4m² - 3mn + 8 - (- m² + 5mn)
= 4m² - 3mn + 8 + m² - 5mn
= 4m² + m² - 3mn - 5mn + 8
= 5m² - 8mn + 8

(vi) -x² + 10x - 5 from 5x - 10

= 5x - 10 - (-x² + 10x - 5)
= 5x - 10 + x² – 10x + 5
= x² + 5x - 10x - 10 + 5
= x² - 5x - 5

(vii) 5a² - 7ab + 5b² from 3ab - 2a² - 2b²

= 3ab - 2a² - 2b² - (5a² - 7ab + 5b²)
= 3ab - 2a² - 2b² - 5a² + 7ab - 5b²
= 3ab + 7ab - 2a² - 5a² - 2b² - 5b²
= 10ab - 7a² - 7b²

(viii) 4pq - 5q² - 3p² from 5p² + 3q² - pq

= 5p² + 3q² - pq - (4pq - 5q² - 3p²)
= 5p² + 3q² - pq - 4pq + 5q² + 3p²
= 5p² + 3p² + 3q² + 5q² - pq - 4pq
= 8p² + 8q² - 5pq

Question 4: (a) What should be added to x² + xy + y² to obtain 2x² + 3xy?

= (x² + xy + y²) + () = 2x² + 3xy
Therefore, required expression to be added.
= (2x² + 3xy) - (x² + xy + y²)
= 2x² + 3xy - x² - xy - y²
= 2x² - x² + 3xy - xy - y²
= 1x² + 2xy - y²

(b) What should be subtracted from 2a + 8b + 10 to get - 3a + 7b + 16?

= (2a + 8b + 10) - () = (- 3a + 7b + 16)
Therefore, the required expression to be subtracted.
= (2a + 8b + 10) - (- 3a + 7b + 16)
= 2a + 8b + 10 + 3a - 7b - 16
= 2a + 3a + 8b - 7b + 10 - 16
= 5a + b - 6

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

= 3x² - 4y² + 5xy + 20 - () = - 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

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

Sum of 3x - y + 11 and - y - 11
= (3x - y + 11) + (- y - 11)
= 3x - y + 11 - y - 11
= 3x - y - y + 11 - 11
= 3x - 2y
From 3x - 2y subtract 3x - y - 11
= (3x - 2y) - (3x - y - 11)
= 3x - 2y - 3x + y + 11
= 3x - 3x - 2y + y + 11
= -y + 11

(b) From the sum of 4 + 3x and 5 - 4x + 2x², subtract the sum of 3x² - 5x and
–x
² + 2x + 5.

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 - 5x - x² + 2x + 5
= 3x² - x² - 5x + 2x + 5
= 2x² - 3x + 5
From 9 - x + 2x² subtract 2x² - 3x + 5
= (9 - x + 2x²) - (2x² - 3x + 5)
= 9 – x + 2x² - 2x² + 3x - 5
= 9 - 5 - x + 3x + 2x² - 2x²
= 4 + 2x

1. Anonymous16 July, 2021

Good

2. Brilliant👍😎