QuestionFactor out the greatest common factor. $7 \times(a+2 b)-(a+2 b)$

Studdy Solution

STEP 1

What is this asking? We're trying to simplify an expression by pulling out the biggest shared piece between two terms. Watch out! Don't forget that $(a + 2b)$ is a single term, just like $x$ or $y$ would be!

STEP 2

1. Rewrite the expression
2. Identify and factor out the GCF

STEP 3

We've got $7 \cdot (a+2b) - (a+2b)$ .
Notice how $(a+2b)$ appears in both parts of our expression?
That's a big clue!
To make it even clearer, let's rewrite the second part.
Remember, anything multiplied by 1 stays the same, so we can write $(a+2b)$ as $1 \cdot (a+2b)$ .
This gives us $7 \cdot (a + 2b) - 1 \cdot (a+2b)$ .
Now the common factor $(a+2b)$ is super obvious!

STEP 4

Now, we factor out $(a+2b)$ .
Imagine $(a+2b)$ is like a golden ticket everyone wants!
Both the 7 and the -1 have this golden ticket, and we're going to take it from them.
When we take $(a+2b)$ from $7 \cdot (a+2b)$ , we're left with just 7.
When we take $(a+2b)$ from $-1 \cdot (a+2b)$ , we're left with $-1$ .
So, we write it like this: $(a+2b)(7-1)$ .

STEP 5

Inside the second set of parentheses, we have $7-1$ , which simplifies to 6.
So, our fully factored expression is $(a+2b) \cdot 6$ , or more conventionally, $6(a+2b)$ .
Boom!

STEP 6

$6(a+2b)$

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