Question

factor by grouping a^2+2ab-24b^2

Answer 1

Factor (by grouping) \[a^2 + 2 a b - 24 b^2\]

What we want to do here to factor a quadratic by grouping is to multiply the coefficient of the highest order term (1) by the coefficient of the lowest order term (-24). 1*-24 = -24.

Now, we factor that quantity, and look for a pair of factors which add to the coefficient of the middle term (2).

-24 = -1*24
-24 = -2*12
-24 = -3*8
-24 = -4*6
-24 = -6*4
-24 = -8*3
-24 = -12*2
-24 = -24*1

Do you see any pairs of factors there which add to 2?