Question

what should be added to 9a²b²-12abc to make a perfect square?​

Answer 1

Given,

Given algebraic expression = 9a²b²-12abc

To find,

The algebraic term which we need to add with the given expression, to make it a perfect square.

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

In such cases, we have to add such a term which will produce (A±B)² form.

Here, we can bring (A-B)² = A²-2AB+B² form,

» 9a²b²-12abc

= (3ab)² - (2×3ab×2c)

Here,the 2AB is (2×3ab×2c) and A is (3ab)

This implies, B is (2c)

Now, we have to add B² or (2c)² = 4c², to complete (A-B)² formula.

So,

9a²b²-12abc+4c²

= (3ab) - (2×3ab×2c) + (2c)²

= (3ab-2c)²

= Perfect square

Hence, we need to add 4c²