Question

M6|L22 Combining Like Terms (Part 3)Sign out
Write the expression in simplest form.
Use the distributive property to write an equivalent expression without parentheses.
(2y+12z)−(7y+2z)
= 2y + 12z +
+
Great job!
Next, write an equivalent expression by grouping all of the like variables together.
=
2y
+
−7y
+
12z
+
−2z
Good work!
Now rewrite the expression with the fewest possible terms.
(2y+12z)−(7y+2z)
= 2y + 12z + −7y + −2z
= 2y + −7y + 12z + −2z
=
Excellent!
Factor to rewrite the expression another way. To start factoring, choose the greatest common factor of −5y and 10z.
(2y+12z)−(7y+2z)
= 2y + 12z + −7y + −2z
= 2y + −7y + 12z + −2z
= −5y+10z

6

5

4
Good work!
Now find the factors that, when multiplied by 5, equal −5y and 10z and fill them in the parentheses to write the factored expression.
(2y+12z)−(7y+2z)
= 2y + 12z + −7y + −2z
= 2y + −7y + 12z + −2z
= −5y+10z
= 5(
+
)

Answer 1

To factor the expression \(-5y + 10z\), we first identify the common factor, which is 5. We can re-write the expression as follows:

\[
-5y + 10z = 5(-y + 2z)
\]

Now, we can fill in the parentheses with \(-y\) and \(2z\):

\[
(2y + 12z) - (7y + 2z) = 2y + 12z - 7y - 2z = -5y + 10z = 5(-y + 2z)
\]

So, the final factored expression is:

\[
5(-y + 2z)
\]