Find the product $(p^{2} - q^{2}) (2 p + q)$

2 p^{2} - q^{2} + p (p - 2 q)

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2 p^{3} + q^{3} + p q (p + q)

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2 p^{3} - q^{3} + p q (p - 2 q)

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p^{2} - q^{2} + p q (p - q)

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Solution

The correct option is C $2 p^{3} - q^{3} + p q (p - 2 q)$
$(p^{2} - q^{2}) (2 p + q)$
$= p^{2} (2 p + q) - q^{2} (2 p + q)$
$= 2 p^{3} + p^{2} q - 2 p q^{2} - q^{3}$

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\frac{d}{d x} [1 + \frac{p}{q} x + \frac{p (p + q)}{2!} {(\frac{x}{q})}^{2} + \frac{p (p + q) (p + 2 q)}{3!} {(\frac{x}{q})}^{3} . . . . \infty] =

Factorise: p^{2} + q^{2} + 2 (p q + q r + r p) .

P_{1}

P_{2}

P = \frac{x}{x + y}, Q = \frac{y}{x + y}

\frac{1}{P - Q} - \frac{2 Q}{P^{2} - Q^{2}}

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