Math  /  Algebra

Question20. 3z3+4z33 z^{3}+4-z^{3}

Studdy Solution

STEP 1

What is this asking? Simplify this expression by combining like terms. Watch out! Don't forget that even though we don't see a number in front of the variable z3z^3, there's actually a **hidden 1** there!

STEP 2

1. Combine the z3z^3 terms.
2. Write out the simplified expression.

STEP 3

First, let's **spot the like terms**: 3z33z^3 and z3-z^3.
Remember, like terms are **terms that have the same variable raised to the same power**!
It's like matching socks – we want to put the identical ones together!

STEP 4

We have 3z33z^3 and z3-z^3, but remember our **hidden 1**!
We can rewrite z3-z^3 as 1z3-1z^3.
So, we have 3z33z^3 and 1z3-1z^3.

STEP 5

Now, let's **combine the coefficients** of our like terms: 33 and 1-1.
What's 3+(1)3 + (-1)?
It's **2**!

STEP 6

Since we're adding and subtracting, we **keep the variable part the same**, which is z3z^3.
So, 3z3+(1)z3=2z33z^3 + (-1)z^3 = 2z^3.

STEP 7

We combined our z3z^3 terms, but we still have that **lonely constant**, 44, hanging around!
Let's bring it down to join the party!

STEP 8

Putting it all together, we get 2z3+42z^3 + 4.
Boom!

STEP 9

2z3+42z^3 + 4

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