Factorize gradually 24p^2 + Pq - 23q^2

Answer 1

To factorize the given expression 24p^2 + pq - 23q^2, we need to find two numbers that multiply to -552 (-24 * 23 = -552) and add up to 1 (the coefficient of the middle term p).

The two numbers that meet these conditions are 24 and -23.

Therefore, we can rewrite the expression as follows:

24p^2 + pq - 23q^2
= 24p^2 + 24pq - 23pq - 23q^2
= 24p(p + q) - 23q(p + q)
= (24p - 23q)(p + q)

So, 24p^2 + pq - 23q^2 can be factorized as (24p - 23q)(p + q).