Question
Consider the expression
6
z
ā
7
8
x
+
4
2
6zā78x+42.
Use the distributive property to generate an expression with
6
6 as a common factor
6
z
ā
7
8
x
+
4
2
6zā78x+42.
Use the distributive property to generate an expression with
6
6 as a common factor
Answers
GPT-4o mini
To factor the expression \( 6z - 78x + 42 \) by using the distributive property, we need to identify the greatest common factor (GCF) of the coefficients in the expression.
1. The coefficients in the expression are:
- For \( 6z \), the coefficient is \( 6 \).
- For \( -78x \), the coefficient is \( -78 \).
- For \( 42 \), the coefficient is \( 42 \).
2. The GCF of \( 6 \), \( -78 \), and \( 42 \) is \( 6 \).
3. Now, we will factor out \( 6 \) from each term in the expression:
\[
6z - 78x + 42 = 6(z) - 6(13x) + 6(7)
\]
This can be rewritten as:
\[
6(z - 13x + 7)
\]
Thus, using the distributive property, the expression \( 6z - 78x + 42 \) can be factored to:
\[
6(z - 13x + 7)
\]
1. The coefficients in the expression are:
- For \( 6z \), the coefficient is \( 6 \).
- For \( -78x \), the coefficient is \( -78 \).
- For \( 42 \), the coefficient is \( 42 \).
2. The GCF of \( 6 \), \( -78 \), and \( 42 \) is \( 6 \).
3. Now, we will factor out \( 6 \) from each term in the expression:
\[
6z - 78x + 42 = 6(z) - 6(13x) + 6(7)
\]
This can be rewritten as:
\[
6(z - 13x + 7)
\]
Thus, using the distributive property, the expression \( 6z - 78x + 42 \) can be factored to:
\[
6(z - 13x + 7)
\]