Question

expand using suitable identity (4a+2b-c)^2​

Answer 1

We can expand this using the identity -

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca$

Comparing the given expression with the above identity we get -

${(4a + 2b + ( - c))}^{2} = ( {4a)}^{2} + ( {2b)}^{2} + { (- c)}^{2} + 2(4a)(2b) + 2(2b)( - c) + 2( - c)(4a)$

After simplifying we get-

$= 16 {a}^{2} + 4 {b}^{2} + {c}^{2} + 16ab - 2bc - 8ca$

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Answer 2

$( {a + b + c}^{2}) = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca$

Compare the given expression with the above identity which we get.

$(4a + 2b + { (- c)}^{2} ) = {(4a)}^{2} + {(2b)}^{2} + {( - c)}^{2} + 2(4a)(2b) + 2(2b)( - c) + 2( - c)(4a)$

After simplifying we get that

${16a}^{2} + {4b}^{2} {c}^{2} + 16ab - 2bc - 8ca$

Hope this will help you dear...