Question

$(2a - 3b - 2c)( {4a}^{2} + {9b}^{2} + {4c}^{2} + 6ab - 6bc + 4ca)$
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Answer 1

Answer:

mate it's to simple .

this is a identity of

$(a^{2}-b^{2}-c^{2} )$

\\so, your answer is \\

$(2a^{2}-3b^{2}-2c^{2})$

hope it helps .

mark it as brainlist

Answer 2

Explanation:

As we Know:

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

$(2a - 3b - 2c)( {4a}^{2} + {9b}^{2} + {4c}^{2} + 6ab - 6bc + 4ca)$

= (2a - 3b - 2c) [(2a)² + (3b)² + (2c)² + 2a*3b - 3b*2c + 2c*2a]

= (2a - 3b - 2c) [(2a)² + (-3b)² + (-2c)² + 2*2a*(-3b) - 2*2a*(-3b) + 2*(-3b)*(-2c) - 2*(-3b)*(-2c) + 2*(-2c)*2a - 2*(-2c)*2a + (2a*3b - 3b*2c + 2c*2a)]

= (2a - 3b - 2c) [ (2a - 3b - 2c)² - 2*2a*(-3b) - 2*(-3b)*(-2c) - 2*(-2c)*2a + (2a*3b - 3b*2c + 2c*2a) ]

= (2a - 3b - 2c) [ (2a - 3b - 2c)² + 12ab - 12bc + 8ac + 6ab - 6bc + 4ac ]

= (2a - 3b - 2c) [(2a - 3b - 2c)² + 18ab - 18bc + 12ac]

<hope it helps>

Thanks!