Expand the following, using suitable identity.
$(m + 2 n - 5 p)^{2}$

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Solution

We have, $(m + 2 n - 5 p)^{2}$
$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$
$= (m)^{2} + (2 n)^{2} + (- 5 p)^{2} + 2 (m) (2 n) + 2 (2 n) (- 5 p) + 2 (m) (- 5 p)$
$= m^{2} + 4 n^{2} + 25 p^{2} + 4 m n - 20 n p - 10 m p$

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Expand the following, using suitable identities: ${(- 2 x + 5 y - 3 z)}^{2}$ .

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