Question

I NEED THE ANSWER TO THIS QUESTION ASAP IF YOU ANSWER IT CORRECTLY I WILL LITERALLY WORSHIP YOU FOREVER:

Simplify the polynomials:
5xyx^3+7yxx^3–5x^2x^3–5x^2zx+3zx^3
Note: The 5x^2zx isn't everything to the right is to the power; only 2 is raised to the power.

Answer 1

12x^4y - 5x^5 - 2x^3z if im not mistake

Answer 2

12x^4y -5x^5 -2x^3z

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