Question

x^2y^2-x+y-72. factorize it​

Answer 1

QUESTION:

• Factorize: x²y² - xy - 72

ANSWER:

To Factorize:

• x²y² - xy - 72

Solution:

We are given that,

⇒ x²y² - xy - 72

⇒ (xy)² - xy - 72

Let, xy be t. So,

⇒ t² - t - 72

Now, we need to split the middle term in such a way, that the sum of the numbers obtained is -1t and product is -72t².

So, the numbers are: +8t and -9t.

Sum: +8t - 9t = -1t

Product: (8t)(-9t) = -72t²

So,

⇒ t² - t - 72

⇒ t² - 9t + 8t - 72

Taking common,

⇒ t(t - 9) + 8(t - 9)

Taking (t - 9) common,

⇒ (t - 9)(t + 8)

So,

⇒ (xy - 9)(xy + 8)

Hence, the factorization of x²y² - xy - 72 yields (xy - 9)(xy + 8) .