Q. 2.     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)  4x^{2}y,-3xy^{2},-5xy^{2},5x^{2}y

          (viii)  3p^{2}q^{2}-4pq+5,-10 p^{2}q^{2},15+9pq+7p^{2}q^{2}

          (ix)  ab-4a,4b-ab,4a-4b

          (x) x^{2}-y^{2}-1,y^{2}-1-x^{2},1-x^{2}-y^{2}

Answers (1)
S Sayak

The given terms are added as follows

\\(i) 3mn + (-5mn) + 8mn + (-4mn)\\ = (3 - 5 + 8 - 4)mn\\ = 2mn

\\(ii) t - 8tz + (3tz - z) + (z - t)\\ = t - 8tz + 3tz - z + z - t\\ = (1 - 1)t + (-8 + 3)tz + (-1 + 1)z\\ = -5tz

\\(iii) -7mn + 5 + (12mn + 2) + (9mn - 8) + (-2mn - 3)\\ = -7mn + 5 + 12mn + 2 + 9mn - 8 - 2mn - 3 \\= (-7 + 12 + 9 - 2)mn + 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 \\= (1 - 1 + 1)a + (1 + 1 -1)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 \\= (14 -7)x + (10 - 10)y + (-12 + 8 + 4)xy - 13 + 18 \\= 7x + 5

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

\\(vii) 4x^2y - 3xy^2 - 5xy^2 + 5x^2y\\ \\= (4 + 5)x^2y + (-3 - 5)xy^2 \\= 9x^2y - 8xy^2

\\(viii) 3p^2q^2 - 4pq + 5 + (-10p^2q^2) + (15 + 9pq + 7p^2q^2) \\= 3p^2q^2 - 4pq + 5 - 10p^2q^2 + 15 + 9pq + 7p^2q^2 \\= (3 - 10 + 7)p^2q^2 + (-4 + 9)pq + 5 + 15 \\= 5pq + 20

\\(ix) ab - 4a + (4b - ab) + (4a - 4b) \\= ab - 4a + 4b - ab + 4a - 4b \\= (1 - 1)ab + (-4 + 4)a + (4 - 4)b \\=0

\\(x)\ x^2 - y^2 - 1 + (y^2 - 1 - x^2) + (1 - x^2 - y^2) \\= (1 - 1 - 1)x^2 + (-1 + 1 - 1)y^2 - 1 - 1 + 1 \\= -x^2 - y^2 - 1

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