Hi Gurpinder,
Step 1: Multiply the coefficients of a^2 and b^2. In this case (12 times -3 = -36)
Step 2: What would be two numbers such that it would yield the product (figured out in step 1) and such that it would add up to yield the coefficient of ab (+5 in this case)
The numbers would be 9 and -4 in this case. 9 times -4 = -36 and 9 + (-4) = 5
Step 3: Split the equation in terms of the numbers figured in step 2
so, the equation becomes 12 a^2 - 4ab + 9 ab - 3b^2
Take out the common items from the first two items. Do the same for the last two items.
it becomes 4a * (3a - b) + 3 * (3a - b). It has thus crystallized into sum of two terms.
Take out the common items from these two terms.
(3a - b) * (4a + 3) is the net equation.
Hope this helps. Please pm me in case you need further clarifications.
Thanks.
Naveenan Ramachandran
4GMAT, Dadar(W) & Ghatkopar(W), Mumbai
