QuestionRewrite the expression as a product of two binomials. $-2 x(-x-6)+6(-x-6)$

Studdy Solution

STEP 1

What is this asking? We need to rewrite this expression by finding two binomials that multiply together to give us the same expression. Watch out! Don't forget to distribute correctly and watch out for those negative signs!
They can be sneaky little things.

STEP 2

1. Factor out the common binomial.
2. Simplify the expression.

STEP 3

Look closely!
Both $-2x$ and $6$ are multiplied by the same binomial: $(-x - 6)$ .
That's our common binomial!
This is just like factoring out a greatest common factor (GCF), except now, our GCF is a binomial!
How cool is that?!

STEP 4

We can factor out $(-x - 6)$ from both terms.
Think of it like this: we're dividing each term by $(-x - 6)$ and putting it out front.
This gives us $(-x - 6)(-2x + 6)$ .
See how we pulled out the $(-x - 6)$ ?
What's left in each term goes into the second set of parentheses.

STEP 5

In the second binomial, $-2x + 6$ , both terms have a common factor of $2$ .
But wait, there's more!
We can actually factor out $-2$ to make the $x$ term positive, which is usually preferred.

STEP 6

Factoring out $-2$ from $-2x + 6$ gives us $-2(x - 3)$ .

STEP 7

Now we can put it all together!
We have $(-x - 6)$ and $-2(x - 3)$ .
So our expression becomes $(-x - 6) \cdot -2(x - 3)$ .

STEP 8

We can multiply the $-2$ by the first binomial, distributing it to both terms.
This gives us $(2x + 12)(x - 3)$ .

STEP 9

Our final factored expression is $(2x + 12)(x - 3)$ !
We've successfully rewritten the original expression as a product of two binomials.

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