Question

Express the following expressions as a perfect square : $4a^2+12ab+9b^2$

Answer 1

Step 1: Find the terms which are perfect squares, we can see that two terms are perfect squares, we can write the equations in the form

$={\left(2a\right)}^2+12ab+{\left(3b\right)}^2$

Step 2: Since we have two terms of complete squares, now check if the middle term is of the form of $2ab$, if $a=2aandb=3b$

$2ab=2\left(2a\right)\left(3b\right)=12ab$

Step 3: Write $12ab$ in the form of $2ab$

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

Step 4: Write the equation in the form of the complete square using ${(a+b)}^2=a^2+2ab+b^2$

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

Hence, the result is ${(2a+3b)}^2$.