Question

Subtract the polynomials ( 6x-12x^3) - (6x ^3+2x-4).

the difference of the polynomials is ______ ?????

Answer 1

-18x³ + 4x + 4

Explanation:

Let's first right the polynomials by decreasing exponent.

`(-12x^3 + 6x) - (6x^3+2x-4)`

Next, we will remove the parentheses. Because this is polynomial subtraction, we must distribute the negative into the terms in the parentheses.

`-12x^3+6x-6x^3-2x+4`

Finally, we combine like terms.

`-18x^3+4x+4`

Answer 2

`\textsf{ The difference of the polynomials is: } \boxed{ \sf -18x^3 + 4x + 4.}`

Explanation:

Let's perform the subtraction of the given polynomials step by step:

`\sf (6x - 12x^3) - (6x^3 + 2x - 4)`

Distribute the negative sign in the second polynomial:

`\sf 6x - 12x^3 - 6x^3 - 2x + 4`

Combine like terms:

`\sf 6x - 2x + 4 - 12x^3 - 6x^3`

Simplify further:

`\sf -12x^3 - 6x^3 + 6x - 2x + 4`

Combine the polynomial terms:

`\sf -18x^3 + 4x + 4`

`\textsf{ So, the difference of the polynomials is:} \boxed{ \sf -18x^3 + 4x + 4.}`