Final answer:
The expression (q²r s²t)(q⁴r² - 6q²rs²t + s⁴t²) has a common factor of q²r within the terms inside the parentheses, yielding the simplified expression (q²r s²t)(qr - 6s²t + s²t²/qr) after factoring out q²r.
Step-by-step explanation:
To factor the expression (q²r s²t)(q⁴r² - 6q²rs²t + s⁴t²), we first need to identify a common factor in all terms of the expression inside the parentheses.
Looking at the terms q⁴r², -6q²rs²t, and s⁴t², we can see that q²r is a common factor. Factoring q²r out of each term, we have:
(q²r s²t)(q⁴r²/q²r - 6q²rs²t/q²r + s⁴t²/q²r)
This simplifies to:
(q²r s²t)(qr - 6s²t + s²t²/qr)
Since s²t²/qr is not a like term with the others due to the presence of t² and the division by qr, we cannot factor it ou