We must rewrite the following expression by factoring the GCF from each expression:
[tex]20x+40xy-50xz\text{.}[/tex]
1) First we factor each coefficient into primes:
[tex]\begin{gathered} 20x=5\cdot2\cdot2\cdot x \\ 40xy=5\cdot2\cdot2\cdot2\cdot x\cdot y \\ 50xz=5\cdot5\cdot2\cdot x\cdot z \end{gathered}[/tex]
2) Now, we group the terms that appear in each expression, which form the GCF:
[tex]\begin{gathered} 20x=5\cdot2\cdot2\cdot x=2\cdot(5\cdot2\cdot x)=2\cdot(10x) \\ 40xy=5\cdot2\cdot2\cdot2\cdot x\cdot y=2\cdot2\cdot y\cdot(5\cdot2\cdot x)=4y\cdot(10x) \\ 50xz=5\cdot5\cdot2\cdot x\cdot z=5\cdot z\cdot(5\cdot2\cdot x)=5z\cdot(10x) \end{gathered}[/tex]
3) Replacing each term of the original expression we have:
[tex]20x+40xy-50xz=2\cdot(10x)+4y\cdot(10x)-5z\cdot(10x)[/tex]
Taking the GCF (10x) as a common factor we get:
[tex]20x+40xy-50xz=10x\cdot(2+4y-5z)[/tex]
Answer
[tex]20x+40xy-50xz=10x\cdot(2+4y-5z)[/tex]
