Q. 3.     Subtract:

            (i)  -5y^{2} from y^{2}

            (ii) 6xy from -12xy

            (iii) (a-b) from (a+b)

            (iv)   a(b-5) from b(5-a)

            (v)  -m^{2}+5mn from 4m^{2}-3mn+8

            (vi)  -x^{2}+10x-5 from 5x-10

            (vii) 5a^{2}-7ab+5b^{2} from 3ab-2a^{2}-2b^{2}

            (viii) 4pq-5q^{2}-3p^{2} from 5p^{2}+3q^{2}-pq

Answers (1)

The given terms are subtracted as follows

(i)

\\ y^2 - (-5y^2) \\= y^2 + 5y^2 \\= 6y^2

(ii)

\\ -12xy - 6xy\\ = -18xy

(iii)

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

(iv)

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

(v)

\\4m^2 - 3mn + 8 - (-m^2 + 5mn) \\= 4m^2 - 3mn + 8 + m^2 - 5mn \\= (4 + 1)m^2 + (-3 - 5)mn + 8 \\= 5m^2 - 8mn + 8

 

(vi)

\\ 5x - 10 - (-x^2 + 10x - 5) \\= 5x - 10 + x^2 - 10x + 5 \\= x^2 + (5 - 10)x - 10 + 5 \\= x^2 - 5x - 5

(vii)

\\ 3ab - 2a^2 - 2b^2 - (5a^2 - 7ab + 5b^2) \\= 3ab - 2a^2 - 2b^2 - 5a^2 + 7ab - 5b^2 \\= (3 + 7)ab + (-2 -5)a^2 + (-2 - 5)b^2 \\= 10ab - 7a^2 - 7b^2
(viii)

\\ 5p^2 + 3q^2 - pq - (4pq - 5q^2 - 3p^2) \\= 5p^2 + 3q^2 - pq - 4pq + 5q^2 + 3p^2 \\= (5 + 3) p^2 + (3 + 5)q^2 + (-1 - 4)pq \\= 8p^2 + 8q^2 - 5pq

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