Question

Expansion of $(2a+3b+4c{)}^2$ is ___________

• A. $4a^2+9b^2+16c^2+12ab+24bc+16ca$
• B. $a^2+b^2+2ca$
• C. $a^2-b^2-2ca$
• D. $a^2-b^2+2ca$

Answer 1

The correct option is A

$4a^2+9b^2+16c^2+12ab+24bc+16ca$

Explanation for the correct otpion:

Expanding the given expression.

We know,

${(x+y+z)}^2=x^2+y^2+z^2+2xy+2yz+2zx$

Here,

$x=2a$

$y=3b$

$z=4c$

Substituting the values in the above formula, we get,

$\Rightarrow {(2a+3b+4c)}^2=(2a{)}^2+{\left(3b\right)}^2+{\left(4c\right)}^2+2(2a\left)\right(3b)+2(3b\left)\right(4c)+2(4c\left)\right(2a)$

On further calculation, we get,

$\Rightarrow 4a^2+9b^2+16c^2+12ab+24bc+16ca$

Therefore, the correct option is $\left(A\right)$