Sure! Let's factorize the given expression step-by-step:
The expression is:
[tex]\[ 6x^2 y - 30 xy^2 + 12 x^2 y^2 \][/tex]
### Step 1: Identify common factors in all terms
Look at each term in the expression:
- [tex]\( 6x^2 y \)[/tex]
- [tex]\( -30 xy^2 \)[/tex]
- [tex]\( 12 x^2 y^2 \)[/tex]
Observe that each term contains the factor [tex]\( 6xy \)[/tex]:
- [tex]\( 6 x y \)[/tex] is common in all terms.
### Step 2: Factor out the common factor
Once we identify [tex]\( 6xy \)[/tex] as a common factor, we can factor it out:
[tex]\[ 6xy (x - 5y + 2 xy) \][/tex]
Now let's recheck the factored expression:
### Step 3: Verify the factored result
Distribute the [tex]\( 6xy \)[/tex] back through the expression to verify:
[tex]\[ 6xy \cdot x = 6x^2 y \][/tex]
[tex]\[ 6xy \cdot (-5y) = -30xy^2 \][/tex]
[tex]\[ 6xy \cdot (2xy) = 12x^2 y^2 \][/tex]
Since these terms match the original expression, the factorization is correct.
So, the factored form of the given expression [tex]\( 6x^2 y - 30 xy^2 + 12 x^2 y^2 \)[/tex] is:
[tex]\[ 6xy(2xy + x - 5y) \][/tex]
This is a simplified version of the original polynomial.
