7gh2+70gh+175

The expression \( 7gh^2 + 70gh + 175 \) can be factored. We can start by factoring out the greatest common factor (GCF) from all the terms.

1. Identify the GCF of the coefficients:

   • The coefficients are 7, 70, and 175. The GCF is 7.

2. Factor out the GCF from the expression: \[ 7(gh^2 + 10gh + 25) \]

Now we will factor the quadratic \( gh^2 + 10gh + 25 \).

3. To factor \( gh^2 + 10gh + 25 \), we look for two numbers that multiply to \( 25 \) (the constant term) and add up to \( 10 \) (the coefficient of \( gh \)). These two numbers are \( 5 \) and \( 5 \).

4. Thus, the expression can be factored as: \[ gh^2 + 10gh + 25 = (gh + 5)(gh + 5) = (gh + 5)^2 \]

5. Combining everything, we have: \[ 7(gh + 5)^2 \]

So, the fully factored form of the expression \( 7gh^2 + 70gh + 175 \) is: \[ \boxed{7(gh + 5)^2} \]