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What number must be added to the expression (16a2 – 12a) to make it a perfect square?

What number must be added to the expression (16a2 – 12a) to make it a perfect square? Correct Answer 9/4

GIVEN:

Expression: (16a2 – 12a)

CONCEPT:

A perfect square will be of the forms: (a2 + b2 + 2ab) or (a2 + b2 – 2ab)

CALCULATION:

Suppose ‘p’ must be added.

So, we can write:

16a2 – 12a + p = (4a)2 – 2 × 4a × 3/2 + (√p)2

If it is a perfect square, it will be of the form: (a2 + b2 – 2ab)

⇒ √p = 3/2

⇒ p = 9/4

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