Q.3 Subtract:
\((i) -5y^2 from y^2 \)
\((ii) 6xy from -12xy \)
\((iii) (a – b) from (a + b) \)
\((iv) a(b – 5) from b(5 – a) \)
\((v) -m^2 + 5mn from 4m^2 – 3mn + 8 \)
\((vi) -x^2 + 10x – 5 from 5x – 10 \)
\((vii) 5a^2 – 7ab + 5b^2 from 3ab – 2a^2 – 2b^2 \)
\((viii) 4pq – 5q^2 – 3p^2 from 5p^2 + 3q^2 – pq \)


Answer :

\((i) -5y^2 from y^2 \)
\(= y^2 – (-5y^2) \)
\(= y^2 + 5y^2 \)
\(= 6y^2\)
\((ii) 6xy from -12xy \)
= -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
= 5a + 5b – 2ab
\((v) -m^2 + 5mn from 4m^2 – 3mn + 8 \)
\(= 4m^2 – 3mn + 8 – (- m^2 + 5mn) \)
\(= 4m^2 – 3mn + 8 + m^2 – 5mn \)
\(= 4m^2 + m^2 – 3mn – 5mn + 8 \)
\(= 5m^2 – 8mn + 8 \)
\((vi) -x^2 + 10x – 5 from 5x – 10 \)
\(= 5x – 10 – (-x^2 + 10x – 5)\)
\(= 5x – 10 + x^2 – 10x + 5 \)
\(= x^2 + 5x – 10x – 10 + 5 \)
\(= x^2 – 5x – 5 \)
\((vii) 5a^2 – 7ab + 5b^2 from 3ab – 2a^2 – 2b^2 \)
\(= 3ab – 2a^2 – 2b^2 – (5a^2 – 7ab + 5b^2)\)
\(= 3ab – 2a^2 – 2b^2 – 5a^2 + 7ab – 5b^2 \)
\(= 3ab + 7ab – 2a^2 – 5a^2 – 2b^2 – 5b^2 \)
\(= 10ab – 7a^2 – 7b^2 \)
\((viii) 4pq – 5q^2 – 3p^2 from 5p^2 + 3q^2 – pq \)
\(= 5p^2 + 3q^2 – pq – (4pq – 5q^2 – 3p^2)\)
\( = 5p^2 + 3q^2 – pq – 4pq + 5q^2 + 3p^2\)
\(= 5p^2 + 3p^2 + 3q^2 + 5q^2 – pq – 4pq \)
\(= 8p^2 + 8q^2 – 5pq \)

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