Question

2. Rewrite by factoring the GCF from each expression.d) 20x + 40xy50xzShow your work here:Anciner

Answer 1

We must rewrite the following expression by factoring the GCF from each expression:

`20x+40xy-50xz\text{.}`

1) First we factor each coefficient into primes:

`\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}`

2) Now, we group the terms that appear in each expression, which form the GCF:

`\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}`

3) Replacing each term of the original expression we have:

`20x+40xy-50xz=2\cdot(10x)+4y\cdot(10x)-5z\cdot(10x)`

Taking the GCF (10x) as a common factor we get:

`20x+40xy-50xz=10x\cdot(2+4y-5z)`

Answer

`20x+40xy-50xz=10x\cdot(2+4y-5z)`