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Add: [tex]\[(-4xz - 15xy) + (20xy - 9yz - 16xz)\][/tex]

Combine like terms to simplify the expression.

Sagot :

GinnyAnswer
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]
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