What is factoring by grouping? When factoring a trinomial by grouping, why is it necessary to write the trinomial in four terms?

Answer 1

product of two binomials will become a trinomial.This is bcz itwo terms of the product are like terms so you can simplify and write them as oe term.When you need to factorize you need to have 4 terms.That is why you split the middle term of the trinomial to get a quadrinomial, then group two terms to get a common factor.

See the example
x2 -6x +9 = 0
split the middle term
x2 -3x -3x +9 =0 now make two groups

x2 -3x -3x +9 =0
x(x-3) -3(x-3) = 0 now take (x-3)
(x-3)(x-3) = 0

Answer 2

)(x-3) = 0

Answer 3

10x+15y=465
x+y=39
x-?
y-?

Answer 4

factor by grouping 20^3+65s^2-60s