The correct option is A p^2 + 4q^2 + r^2 4pq 4qr + 2rp Using #160; (a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2qc (p 2q+r)^2 =p^2+4q^2+r^2 4pq 4qr+ ...

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Algebraic Identities

Expand p - ...

Question

Expand $(p - 2 q + r)^{2}$

p^{2} + 4 q^{2} + r^{2} - 4 p q - 4 q r + 2 r p

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p^{2} - 4 q^{2} + r^{2} - 4 p q - 4 q r + 2 r p

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p^{2} + 4 q^{2} - r^{2} - 4 p q - 4 q r + 2 r p

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None of these

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Solution

The correct option is A $p^{2} + 4 q^{2} + r^{2} - 4 p q - 4 q r + 2 r p$
Using $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 a c$ ,
Here $a = p, b = - 2 q$ and $c = r$
$∴ (p - 2 q + r)^{2} = (p)^{2} + (- 2 q)^{2} + (r)^{2} + 2 (p) (- 2 q) + 2 (- 2 q) (r) + 2 (p) (r)$
$= p^{2} + 4 q^{2} + r^{2} - 4 p q - 4 q r + 2 p r$
Hence, $(p - 2 q + r)^{2} = p^{2} + 4 q^{2} + r^{2} - 4 p q - 4 q r + 2 p r$

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