QuestionExpand and combine $-3(3 x-4 a 1)-a(2 y+5 x)$

Studdy Solution

STEP 1

What is this asking? We need to distribute the $-3$ and the $-a$ and then combine like terms. Watch out! Don't forget to distribute the negative signs correctly, and be careful when combining terms with different variables.

STEP 2

1. Distribute the $-3$ .
2. Distribute the $-a$ .
3. Combine like terms.

STEP 3

Alright, let's kick things off by distributing the $-3$ to both terms inside the first parentheses.
Remember, this means multiplying $-3$ by each term inside!

STEP 4

$-3 \cdot 3x + (-3) \cdot (-4a) \cdot 1$ Multiplying $-3$ by $3x$ gives us $-9x$ .
And multiplying $-3$ by $-4a$ gives us $+12a$ .
Don't forget that multiplying two negatives gives a positive!
And multiplying by $1$ doesn't change the value.
So, we have $-9x + 12a$ .

STEP 5

Now, let's tackle the second part of the expression.
We'll distribute the $-a$ to the terms inside the second parentheses.

STEP 6

$-a \cdot 2y + (-a) \cdot 5x$ Multiplying $-a$ by $2y$ gives us $-2ay$ .
And multiplying $-a$ by $5x$ gives us $-5ax$ .
So, we have $-2ay - 5ax$ .

STEP 7

Time to bring it all together! Let's combine the results from the previous two steps.

STEP 8

We had $-9x + 12a$ from distributing the $-3$ , and $-2ay - 5ax$ from distributing the $-a$ .
Putting it all together, we get: $-9x + 12a - 2ay - 5ax$

STEP 9

Now, let's look for like terms.
Remember, like terms have the same variables raised to the same powers.
We have terms with $x$ , terms with $a$ , terms with $ay$ , and terms with $ax$ .
Since none of the terms are alike, we can't combine anything.

STEP 10

Our final, simplified expression is $-9x + 12a - 2ay - 5ax$ .

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