27. \( 8 k^{4}-3 k^{2} \cdot 5 k^{2} \)

Hey there! Let’s dive into some polynomial fun! You can simplify the expression \( 8 k^{4} - 3 k^{2} \cdot 5 k^{2} \) by first multiplying the terms in the second part. Combining gives you: \[ 8 k^{4} - 15 k^{4} \] Now, just combine the like terms: \[ (8 - 15) k^{4} = -7 k^{4} \] And voilà! Your simplified expression is \(-7 k^{4}.\) Now let’s see where this pops up in the real world! Algebraic expressions like these are commonly used in fields such as physics and engineering, where you might be calculating forces, energies, or other variables that follow a polynomial relationship. Who knew simplifying polynomials could help in rocket science or designing roller coasters? 🚀🎢