Question

Expand :
(a+3b+4c)^2​

Answer 1

Question

Expand equation. .

$(a + 3b + 4c)^{2}$

Simplification 1.

Detailed step by step method for beginners..

STEP 1 : Expand the square

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

$= (a+3b+4c) + 3(a+3b+4c)$

STEP 2 : Distribute

$= (a+3b+4c)(a+3b+4c)$

$= (a+3b+4c)+3b(a+3b+4c)+4c(a+3b+4c)$

$= a(a+3b+4c)+3b(a+3b+4c)+4c(a+3b+4c)$

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

$= a^{2}+3ab+4c+3b(a+3b+4c)+4c(a+3b + 4c)$

STEP 3 : Combine like terms

=a²+6ab + 8ac +9b²+12bc + 16c²

=a²+9b²+16c²+6ab+24bc+16ca

[ Answer ]

Simplification 2.

Simple, short answer .....

We know,

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

Here,

x=a

y=3b

z=4c

Putting Values in Identity, We get :

⇒ (a+3b+4c) ²

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

=> =a²+9b²+16c²+6ab+24bc+16ca [Answer]

Note : The above simplification has been done bt two process you can go with any one of your choice..

Hope it helps..

pls mark me as Brainliest and pls give me thanks because I have worked very hard for giving your solution..and pls mark me as Brainliest.

Thank you have a nice day ahead