Question

Subtract the polynomials then simplify: 5x^5+4x^2-2x^6+6x^4 and 10x^2+10x^3+8x^6-9x^4

Answer 1

-10x^6+5x^5+15x^4-10x^3-6x^2.

Step.by-step explanation:

5x^5+4x^2-2x^6+6x^4 - (10x^2+10x^3+8x^6-9x^4).

First distribute the negative over the parentheses:

=5x^5+4x^2-2x^6+6x^4 - 10x^2-10x^3-8x^6+9x^4

Now bring like terms together:

= -2x^6-8x^6+5x^5+6x^4+9x^4-10x^3+4x^2-10x^2

= -10x^6+5x^5+ 15x^4-10x^3-6x^2.

Answer 2

`\large\boxed{-10x^6+5x^5+15x^4-10x^3-6x^2}`

Explanation:

`(5x^5+4x^2-2x^6+6x^4)-(10x^2+10x^3+8x^6-9x^4)\\\\=5x^5+4x^2-2x^6+6x^4-10x^2-10x^3-8x^6-(-9x^4)\\\\=5x^5+4x^2-2x^6+6x^4-10x^2-10x^3-8x^6+9x^4\\\\\text{combine like terms}\\\\=(-2x^6-8x^6)+5x^5+(6x^4+9x^4)-10x^3+(4x^2-10x^2)\\\\=-10x^6+5x^5+15x^4-10x^3-6x^2`