You have to explain that factoring means to convert a combination of additions and/or subtractions of algebraic terms into a PRODUCT.
Under such premises, the use of the distributive property *in REVERSE form) is critical.
You should make clear that the first step consists in finding the COMMON factors for all terms. That is, the IDENTICAL factors that appear in ALL terms of the algebraic expression.
Then, given : - 4 x y - 12 x z + 20 x w
We start by writing all the numbers in each term as an expression of product of PRIME numbers:
- 4 = -1 * 2 * 2
- 12 = -1 * 2 * 2 * 3
20 = 2 * 2 * 5
then we look into what factors are common to all these three numbers. The answer is: 2 * 2 (4) is found common in all prime factor forms. Therefore, the factor "4" is going to be part of the factor we will be extracting.
Now the letter factors:
x y = x * y
x z = x * z
x w = x * w
So, the COMMON factor to all three letter expressions is "x".
Then we are going to extract "4 x" (4 times x) as factor common to all. This is similar to "divide"each term by "4 x".
then we do:
- 4 x y - 12 x z + 20 x w = 4 x ( - y - 3 z + 5 w)
The common extracted factor appears in bold outside the parenthesis, and we are lft inside the parqnthesis with the factors that were NOT common.
The explanation should continue with the "checking" of the correctness of the procedure performed. This is done by using now the Distributive Property aga\gain but to get rid of the parenthesis, and multiplying each term inside by the factor "4x" that we extracted, thus confirming that we get to the starting expression.