Question

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

• A. $a^2+4b^2+9c^2+4ab+12bc+6ac$
• B. $a^2+4b^2+9c^2+4ab+12bc+12ac$
• C. $a^2+4b^2+9c^2+8ab+12bc+6ac$
• D. $a^2+4b^2+9c^3+4ab+12bc+6ac$

Answer 1

The correct option is A

$a^2+4b^2+9c^2+4ab+12bc+6ac$

We use the identity $(a+b+c{)}^2$ = $a^2+b^2+c^2+2ab+2bc+2ca$

Replacing the value of a,b,and c with a,2b, and 3c respectively.

We get $(a+2b+3c{)}^2$ = $a^2+(2b{)}^2+(3c{)}^2+4ab+12bc+6ac$

= $a^2+4b^2+9c^2+4ab+12bc+6ac$