##### 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, -10p2q2, 15 + 9pq + 7p2q2(ix) ab - 4a, 4b – ab, 4a - 4b(x) x2 - y2 – 1, y2 - 1 - x2, 1 - x2 - y2

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

= 3mn - 5mn + 8mn - 4mn

= 2mn

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

= t - 8tz + 3tz - z + z - t

=t - t - z + z - 8tz + 3tz

= -5tz

(iii) (-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 - 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 - 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

= 3m - 4n - 3mn - 3

(vii) 4x2y + (-3xy2) + (-5xy2) + 5x2y

=4x2y - 3xy2 - 5xy2 +5x2y

=4x2y + 5x2y - 3xy2 - 5xy2

= 9x2y - 8xy2

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

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

= 3p2q2 - 10p2 q2 + 7p2q2 - 4pq + 9pq + 5 + 15

= 5pq + 20

(ix) (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 - x2 - x2 - y2 + y2 - y2 - 1 - 1

= -x2 - y2 - 1

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