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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)

best_answer

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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