Subtract $4 p q - 5 q^{2} - 3 p^{2}$ from $5 p^{2} + 3 q^{2} - p q$

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Solution

Find the subtraction of $4 p q - 5 q^{2} - 3 p^{2}$ from $5 p^{2} + 3 q^{2} - p q$
$(5 p^{2} + 3 q^{2} - p q) - (4 p q - 5 q^{2} - 3 p^{2}) = 5 p^{2} + 3 q^{2} - p q - 4 p q + 5 q^{2} + 3 p^{2} (A f t e r r e m o v i n g t h e b r a c k e t t h e s i g n o f s e c o n d b r a c k e t c h a n g e) = 5 p^{2} + 3 p^{2} + 3 q^{2} + 5 q^{2} - p q - 4 p q = 8 p^{2} + 8 q^{2} - 5 p q$
$∴$ The subtraction of $4 p q - 5 q^{2} - 3 p^{2}$ from $5 p^{2} + 3 q^{2} - p q$ is $8 p^{2} + 8 q^{2} - 5 p q$

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Show that

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(iii)

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4 p q - 5 q^{2} - 3 p^{2}

5 p^{2} + 3 q^{2} - p q

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