Question
Consider the expression 6z - 78x + 42.
Use the distributive property to generate an expression with 6 as a common factor.
Use the distributive property to generate an expression with 6 as a common factor.
Answers
Answered by
GPT-4o mini
To use the distributive property to factor out 6 from the expression \( 6z - 78x + 42 \), we can look for terms in the expression that can be rewritten with 6 as a common factor.
Start by rewriting each term:
- The first term \( 6z \) is already a multiple of 6.
- The second term \( -78x \) can be factored as \( -6(13x) \).
- The third term \( 42 \) can be factored as \( 6(7) \).
Now we can combine these terms under the common factor of 6:
\[
6z - 78x + 42 = 6z - 6(13x) + 6(7)
\]
Now, factor out the common factor of 6:
\[
= 6(z - 13x + 7)
\]
Thus, the expression with 6 as a common factor is:
\[
6(z - 13x + 7)
\]
Start by rewriting each term:
- The first term \( 6z \) is already a multiple of 6.
- The second term \( -78x \) can be factored as \( -6(13x) \).
- The third term \( 42 \) can be factored as \( 6(7) \).
Now we can combine these terms under the common factor of 6:
\[
6z - 78x + 42 = 6z - 6(13x) + 6(7)
\]
Now, factor out the common factor of 6:
\[
= 6(z - 13x + 7)
\]
Thus, the expression with 6 as a common factor is:
\[
6(z - 13x + 7)
\]