Question 127

What number must be added to the expression $$16a^{2} -12a$$ to make it a perfect square ?

Solution

Using the rule, $$a^2 - 2ab + b^2 = (a-b)^2$$

=> $$16a^2 - 12a = (4a)^2 - 2*4a*\frac{3}{2}$$

= $$(4a)^2 - 2*4a*\frac{3}{2} + (\frac{3}{2})^2 - \frac{9}{4}$$

= $$(4a - \frac{3}{2})^2$$

=> $$\frac{9}{4}$$ should be added to make the above expression a perfect square.

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