To find the resulting polynomial from the expression [tex]\( 5x^4y^3 - x^5y^4 \)[/tex], let's break it down step-by-step:
1. Understanding Terms:
- The first term is [tex]\( 5x^4y^3 \)[/tex]. This term consists of a coefficient of 5, with [tex]\( x \)[/tex] raised to the power of 4 and [tex]\( y \)[/tex] raised to the power of 3.
- The second term is [tex]\( -x^5y^4 \)[/tex]. This term has a coefficient of -1, with [tex]\( x \)[/tex] raised to the power of 5 and [tex]\( y \)[/tex] raised to the power of 4.
2. Combining Like Terms:
- In this expression, there are no like terms to combine because:
- The term [tex]\( 5x^4y^3 \)[/tex] has [tex]\( x \)[/tex] and [tex]\( y \)[/tex] raised to different powers compared to [tex]\( -x^5y^4 \)[/tex].
3. Simplifying the Expression:
- Since the terms [tex]\( 5x^4y^3 \)[/tex] and [tex]\( -x^5y^4 \)[/tex] are not like terms, the expression remains:
[tex]\[ 5x^4y^3 - x^5y^4 \][/tex]
Thus, the final result of the polynomial is [tex]\( -x^5y^4 + 5x^4y^3 \)[/tex].
