Sure, let's add the given polynomials step by step:
We have the polynomials:
[tex]\[ (-4xz - 15xy) \][/tex]
and
[tex]\[ (20xy - 9yz - 16xz) \][/tex]
Step 1: Identify and group the like terms from each polynomial. Like terms have the same variables raised to the same power.
- The terms with [tex]\( xy \)[/tex]:
[tex]\[ -15xy \][/tex]
[tex]\[ 20xy \][/tex]
- The terms with [tex]\( xz \)[/tex]:
[tex]\[ -4xz \][/tex]
[tex]\[ -16xz \][/tex]
- The term with [tex]\( yz \)[/tex]:
[tex]\[ -9yz \][/tex]
Step 2: Combine the like terms:
- For the [tex]\( xy \)[/tex] terms:
[tex]\[ -15xy + 20xy = 5xy \][/tex]
- For the [tex]\( xz \)[/tex] terms:
[tex]\[ -4xz - 16xz = -20xz \][/tex]
- The [tex]\( yz \)[/tex] term remains as it is because there is only one [tex]\( yz \)[/tex] term:
[tex]\[ -9yz \][/tex]
Step 3: Write down the combined expression:
So,
[tex]\[ (-4xz - 15xy) + (20xy - 9yz - 16xz) \][/tex]
Simplifies to:
[tex]\[ 5xy - 20xz - 9yz \][/tex]
Therefore, the result of the addition is:
[tex]\[ 5xy - 20xz - 9yz \][/tex]
