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

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