I need to factor out the greatest common monomial factor:
1) 20x^2y^2 - 4xy
2) 18s^2t^5 - 2s^3t
3) -2g^4 +14g^2 + 6g
To factor out the greatest common monomial factor, follow these steps:
1) Identify the terms in the expression.
2) Determine the variables in each term and find the highest power of each variable that appears.
Let's go through the examples you provided:
1) For 20x^2y^2 - 4xy:
The terms are 20x^2y^2 and -4xy.
The highest power of x is 2 and the highest power of y is 2.
The greatest common monomial factor is 4xy.
Factoring out 4xy, we get:
20x^2y^2 - 4xy = 4xy(5xy - 1)
2) For 18s^2t^5 - 2s^3t:
The terms are 18s^2t^5 and -2s^3t.
The highest power of s is 3 and the highest power of t is 5.
The greatest common monomial factor is 2s^2t.
Factoring out 2s^2t, we get:
18s^2t^5 - 2s^3t = 2s^2t(9t^4 - s)
3) For -2g^4 + 14g^2 + 6g:
The terms are -2g^4, 14g^2, and 6g.
The highest power of g is 4.
The greatest common monomial factor is 2g.
Factoring out 2g, we get:
-2g^4 + 14g^2 + 6g = 2g(-g^3 + 7g + 3)
Note that the factorization may not always lead to further simplification, but it helps to identify the greatest common monomial factor in order to simplify expressions or solve certain equations.