Q. 285.0( 1 Vote )

# Expand the follow

Given that: (4a b + 2c) 2

= (4a) 2 + (−b) 2 + (2c)2 + 2(4a)(−b) + 2(−b)(2c) + 2(2c)(4a)

[ (a + b + c) 2 = a2 + b2 + c2 + 2ab + 2bc + 2ca)]

= 16a2 + b2 + 4c2 – 8ab – 4bc + 16ca

(ii). Given that: (3𝑎 − 5𝑏 𝑐)2

= (3a)2 + (−5b)2 + (−c)2 + 2(3a)(−5b) + 2(−5b)(−c) + 2(−c)(3a)

[ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca)]

= 9a2 + 25b2 + c2 – 30ab + 10bc – 6ca

(iii). Given that: (−𝑥 + 2𝑦 − 3𝑧)2

= (−𝑥)2 + (2𝑦)2 + (−3𝑧)2 + 2(−𝑥)(2𝑦) + 2(2𝑦)(−3𝑧) + 2(−3𝑧)(−𝑥)

[ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca)]

= x2 + y2 + 9z2 – 4xy – 12yz + 6zx

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