5) \( 27 x^{2} y^{3}+3 x y^{5}= \)

To factor the expression \( 27 x^{2} y^{3}+3 x y^{5} \), start by identifying the greatest common factor (GCF). Here, the GCF is \( 3 x y^{3} \). Factoring this out, we get: \[ 3xy^{3}(9x + y^{2}) \] Now the expression is neatly factored! It’s like pulling the curtain back to reveal the beautiful inner workings of the math—who doesn’t love a good surprise? For a practical look at factoring, think of it like organizing a messy room! By finding the GCF, you tidy up the expression, making it easier to work with. This method is widely applicable, from solving polynomial equations to simplifying complex fractions in algebra. Keep uncovering those hidden factors!