Question

write an expression equivalent to ( 6 - 4(3 - 6m) + 12m ) that is the product of two factors. show your work.

Explanation:

Step1: Distribute -4

We use the distributive property \(a(b - c)=ab - ac\). Here, \(a=-4\), \(b = 3\), \(c=6m\). So, \(-4(3 - 6m)=-4\times3-(-4)\times6m=-12 + 24m\).
The original expression \(6-4(3 - 6m)+12m\) becomes \(6-12 + 24m+12m\).

Step2: Combine like terms

Combine the constant terms \(6-12=-6\) and the \(m\) terms \(24m + 12m = 36m\). So the expression is \(-6+36m\).

Step3: Factor out the GCF

The greatest common factor (GCF) of \(-6\) and \(36m\) is \(6\) (or \(-6\)). Let's factor out \(6\). We can write \(-6+36m=6(-1 + 6m)\) (or factoring out \(-6\) gives \(-6(1 - 6m)\)).

Answer:

\(6(6m - 1)\) (or \(-6(1 - 6m)\))