Question

find the expansion of (2a+3b+4c)^2​

Answer 1

We know,

(x+y+z)2=x2+y2+z2+2xy+2yz+2zx        [Identity]

Here, 

x=2a

y=3b

z=4c

Putting Values in Identity, We get :

⇒ (2a+3b+4c)2=(2a)2+(3b)2+(4c)2+2(2a)(3b)+2(3b)(4c)+2(4c)(2a)

                                  =4a2+9b2+16c2+12ab+24bc+16ca ( answer)

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Answer 2

$\large\underline{\sf{Solution-}}$

Given expansion is

$\rm :\longmapsto\: {(2a + 3b + 4c)}^{2}$

We know that,

$\boxed{ \sf{ \: {(x + y + z)}^{2} = {x}^{2} + {y}^{2} + {z}^{2} + 2xy + 2yz + 2zx}}$

So, here

$\red{\rm :\longmapsto\:x = 2a}$

$\red{\rm :\longmapsto\:y = 3b}$

$\red{\rm :\longmapsto\:z = 4c}$

So, on substituting the values of x, y and z, we get

$\rm :\longmapsto\: {(2a + 3b + 4c)}^{2}$

$\rm \: = \: {(2a)}^{2} + {(3b)}^{2} + {(4c)}^{2} + 2(2a)(3b) + 2(3b)(4c) + 2(4c)(2a)$

$\rm \: = \: {4a}^{2} + {9b}^{2} + {16c}^{2} + 12ab + 24bc + 16ca$

Additional Information :-

$\boxed{ \bf{ \: {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy}}$

$\boxed{ \bf{ \: {(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy}}$

$\boxed{ \bf{ \: {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y)}}$

$\boxed{ \bf{ \: {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}}$

$\boxed{ \bf{ \: {x}^{2} - {y}^{2} = (x + y)(x - y)}}$

$\boxed{ \bf{ \: {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2})}}$

$\boxed{ \bf{ \: {x}^{3} - {y}^{3} = (x - y)( {x}^{2} + xy + {y}^{2})}}$

$\boxed{ \bf{ \: {x}^{4} - {y}^{4} = (x - y)(x + y)( {x}^{2} + {y}^{2})}}$