Add the following expressions:
$p^{2} - 5 p q - q^{2}$ and $- 3 p^{2} + 2 p q - 2 p^{2}$

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Solution

$(p^{2} - 5 p q - q^{2}) + (- 3 p^{2} + 2 p q - 2 p^{2})$
$= p^{2} - 5 p q - q^{2} - 3 p^{2} + 2 p q - 2 p^{2}$
$= (p^{2} - 3 p^{2} - 2 p^{2}) + (2 p q - 5 p q) - q^{2}$
$= - 4 p^{2} - 3 p q - q^{2}$
$= - (4 p^{2} + 3 p q + q^{2})$
Hence the correct answer is $- (4 p^{2} + 3 p q + q^{2})$ .

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Question 57 (a)

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p^{2} + q^{2} + r^{2} + 2 p q + 2 q r + 2 r p

Find each of the following products:

$(3 p^{2} + q^{2}) \times (2 p^{2} - 3 q^{2})$

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