The correct option is A 36p^2+ 25q^2+ 16r^2 60pq +40qr 48rp We know (a + #160;b #160;+ #160;c)^2 #160;= a^2 + b^2 + #160;c^2 #160;+ #1 ...

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Algebraic Identities

Expand 6p -...

Question

Expand $(6 p - 5 q - 4 r)^{2}$

36 p^{2} + 25 q^{2} + 16 r^{2} - 60 p q + 40 q r - 48 r p

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36 p^{2} + 15 q^{2} + 16 r^{2} - 60 p q + 40 q r - 48 r p

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36 p^{2} + 55 q^{2} + 16 r^{2} - 60 p q + 40 q r + 48 r p

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36 p^{2} + 95 q^{2} + 16 r^{2} - 60 p q + 40 q r + 48 r p

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Solution

The correct option is A $36 p^{2} + 25 q^{2} + 16 r^{2} - 60 p q + 40 q r - 48 r p$
We know $(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
Hence

$(6 p - 5 q - 4 r)^{2} = (6 p)^{2} + (- 5 q)^{2} + (- 4 r)^{2} + 2 \times (6 p) \times (- 5 q) + 2 \times (- 5 q) \times (- 4 r) + 2 \times (- 4 r) \times (6 p)$
$= 36 p^{2} + 25 q^{2} + 16 r^{2} - 60 p q + 40 q r - 48 r p$

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