Answer :
Sure! Let's factor out the indicated numbers from each expression step-by-step.
16. Factor [tex]\(-\frac{1}{3}\)[/tex] out of [tex]\(-\frac{1}{3}x - 12\)[/tex].
1. Start with the expression [tex]\(-\frac{1}{3}x - 12\)[/tex].
2. Notice that both terms need to be divided by [tex]\(-\frac{1}{3}\)[/tex] to factor it out:
[tex]\[
-\frac{1}{3}x - 12 = -\frac{1}{3}(x + 36)
\][/tex]
3. To verify, distribute [tex]\(-\frac{1}{3}\)[/tex]:
[tex]\[
-\frac{1}{3}(x + 36) = -\frac{1}{3}x - \frac{1}{3} \times 36 = -\frac{1}{3}x - 12
\][/tex]
So, the factored form is [tex]\(x + 36\)[/tex].
17. Factor [tex]\(-\frac{1}{6}\)[/tex] out of [tex]\(-\frac{1}{3}x + \frac{5}{6}y\)[/tex].
1. Begin with the expression [tex]\(-\frac{1}{3}x + \frac{5}{6}y\)[/tex].
2. Divide each term by [tex]\(-\frac{1}{6}\)[/tex]:
[tex]\[
-\frac{1}{3}x + \frac{5}{6}y = -\frac{1}{6}(2x - 5y)
\][/tex]
3. Check by distributing [tex]\(-\frac{1}{6}\)[/tex]:
[tex]\[
-\frac{1}{6}(2x - 5y) = -\frac{1}{6} \times 2x + \frac{1}{6} \times 5y = -\frac{1}{3}x + \frac{5}{6}y
\][/tex]
So, the factored expression is [tex]\(2x - 5y\)[/tex].
18. Factor [tex]\(-\frac{1}{2}\)[/tex] out of [tex]\(-\frac{1}{2}x + 8\)[/tex].
1. Start with [tex]\(-\frac{1}{2}x + 8\)[/tex].
2. Divide each term by [tex]\(-\frac{1}{2}\)[/tex]:
[tex]\[
-\frac{1}{2}x + 8 = -\frac{1}{2}(x - 16)
\][/tex]
3. Confirm by distributing [tex]\(-\frac{1}{2}\)[/tex]:
[tex]\[
-\frac{1}{2}(x - 16) = -\frac{1}{2}x + \frac{1}{2} \times 16 = -\frac{1}{2}x + 8
\][/tex]
Hence, the expression simplifies to [tex]\(x - 16\)[/tex].
So, the factored expressions are:
1. [tex]\(-\frac{1}{3}x - 12\)[/tex] becomes [tex]\(x + 36\)[/tex]
2. [tex]\(-\frac{1}{3}x + \frac{5}{6}y\)[/tex] becomes [tex]\(2x - 5y\)[/tex]
3. [tex]\(-\frac{1}{2}x + 8\)[/tex] becomes [tex]\(x - 16\)[/tex]
16. Factor [tex]\(-\frac{1}{3}\)[/tex] out of [tex]\(-\frac{1}{3}x - 12\)[/tex].
1. Start with the expression [tex]\(-\frac{1}{3}x - 12\)[/tex].
2. Notice that both terms need to be divided by [tex]\(-\frac{1}{3}\)[/tex] to factor it out:
[tex]\[
-\frac{1}{3}x - 12 = -\frac{1}{3}(x + 36)
\][/tex]
3. To verify, distribute [tex]\(-\frac{1}{3}\)[/tex]:
[tex]\[
-\frac{1}{3}(x + 36) = -\frac{1}{3}x - \frac{1}{3} \times 36 = -\frac{1}{3}x - 12
\][/tex]
So, the factored form is [tex]\(x + 36\)[/tex].
17. Factor [tex]\(-\frac{1}{6}\)[/tex] out of [tex]\(-\frac{1}{3}x + \frac{5}{6}y\)[/tex].
1. Begin with the expression [tex]\(-\frac{1}{3}x + \frac{5}{6}y\)[/tex].
2. Divide each term by [tex]\(-\frac{1}{6}\)[/tex]:
[tex]\[
-\frac{1}{3}x + \frac{5}{6}y = -\frac{1}{6}(2x - 5y)
\][/tex]
3. Check by distributing [tex]\(-\frac{1}{6}\)[/tex]:
[tex]\[
-\frac{1}{6}(2x - 5y) = -\frac{1}{6} \times 2x + \frac{1}{6} \times 5y = -\frac{1}{3}x + \frac{5}{6}y
\][/tex]
So, the factored expression is [tex]\(2x - 5y\)[/tex].
18. Factor [tex]\(-\frac{1}{2}\)[/tex] out of [tex]\(-\frac{1}{2}x + 8\)[/tex].
1. Start with [tex]\(-\frac{1}{2}x + 8\)[/tex].
2. Divide each term by [tex]\(-\frac{1}{2}\)[/tex]:
[tex]\[
-\frac{1}{2}x + 8 = -\frac{1}{2}(x - 16)
\][/tex]
3. Confirm by distributing [tex]\(-\frac{1}{2}\)[/tex]:
[tex]\[
-\frac{1}{2}(x - 16) = -\frac{1}{2}x + \frac{1}{2} \times 16 = -\frac{1}{2}x + 8
\][/tex]
Hence, the expression simplifies to [tex]\(x - 16\)[/tex].
So, the factored expressions are:
1. [tex]\(-\frac{1}{3}x - 12\)[/tex] becomes [tex]\(x + 36\)[/tex]
2. [tex]\(-\frac{1}{3}x + \frac{5}{6}y\)[/tex] becomes [tex]\(2x - 5y\)[/tex]
3. [tex]\(-\frac{1}{2}x + 8\)[/tex] becomes [tex]\(x - 16\)[/tex]
