Answer:
12x^4y -5x^5 -2x^3z
Step-by-step explanation:
The rule for exponents is (a^b)(a^c) = a^(b+c). Simply add the exponents of each of the variables in each term. Then examine the terms to see which are "like" terms (have the same constellation of variables). Combine those.
5xyx^3+7yxx^3–5x^2x^3–5x^2zx+3zx^3
= 5x^(1+3)y +7x^(1+3)y -5x^(2+3) -5x(2+1)z +3x^3z
= 5x^4y +7x^4y -5x^5 -5x^3z +3x^3z
= (x^4y)(5+7) -5x^5 +(x^3z)(-5+3)
= 12x^4y -5x^5 -2x^3z
We often like to write these with the variable constellations in dictionary order and by decreasing degree, so ...
-5x^5 +12x^4y -2x^3z
