To factor the expression [tex]\(80p + 30q\)[/tex], we need to follow a series of steps to find a common factor and write the expression in a factored form. Here is a detailed, step-by-step solution:
1. Identify the coefficients:
The coefficients in the expression [tex]\(80p + 30q\)[/tex] are 80 and 30.
2. Find the greatest common factor (GCF):
To factor the expression, we first determine the greatest common factor (GCF) of the coefficients 80 and 30. The GCF is the largest positive integer that can evenly divide both numbers.
- Factors of 80: [tex]\(1, 2, 4, 5, 8, 10, 16, 20, 40, 80\)[/tex]
- Factors of 30: [tex]\(1, 2, 3, 5, 6, 10, 15, 30\)[/tex]
- The greatest common factor of 80 and 30 is 10.
3. Factor out the GCF:
Now that we know the GCF is 10, we can factor it out from the expression:
[tex]\[
80p + 30q = 10 \cdot 8p + 10 \cdot 3q
\][/tex]
We factored 10 out from each term.
4. Write the expression in factored form:
After factoring out the greatest common factor, we use the distributive property to write the expression in a factored form:
[tex]\[
80p + 30q = 10(8p) + 10(3q) = 10(8p + 3q)
\][/tex]
Thus, the factored form of the expression [tex]\(80p + 30q\)[/tex] is:
[tex]\[
\boxed{10(8p + 3q)}
\][/tex]
