Question

Subtract. (3x2 2?x3)?(?5x3 2x2 1) express the answer in standard form. enter your answer in the box.

Answer 1

To subtract the expression
`(3x^2 - 2x^3) - (-5x^3 + 2x^2 + 1)`, distribute the negative sign and combine like terms to obtain
`x^2 + 3x^3 - 1` in standard form.

Step-by-step explanation:

To subtract the expression
`(3x^2 - 2x^3) - (-5x^3 + 2x^2 + 1)`, you need to distribute the negative sign to all terms within the parentheses. Then, combine like terms.

`(3x^2 - 2x^3) - (-5x^3 + 2x^2 + 1) = 3x^2 - 2x^3 + 5x^3 - 2x^2 - 1`.

Next, combine like terms by grouping the
`x^3` terms and the
`x^2` terms together:
`3x^2 - 2x^3 + 5x^3 - 2x^2 - 1 = (3x^2 - 2x^2) + (-2x^3 + 5x^3) - 1.`

Simplify the expression further:
`x^2 + 3x^3 - 1`.

Therefore, the answer in standard form is
`x^2 + 3x^3 - 1.`

Answer 2

To perform the subtraction, distribute the negative sign to each term of the second polynomial and then combine like terms. The final expression in standard form is 3
`x^3` +
`x^2` - 1.

Step-by-step explanation:

The question asks to subtract two polynomials and express the answer in standard form. We approach this problem by changing the sign of each term in the polynomial being subtracted and then combining like terms. When subtracting polynomials, remember to distribute the subtraction to each term in the second polynomial.

Here is how we can solve the given expression:

(3
`x^2` – 2
`x^3`) – (– 5
`x^3` + 2
`x^2` + 1)

The first step is distributing the negative sign across the second polynomial:

3
`x^2` – 2
`x^3` – (– 5
`x^3`) – 2
`x^2` – 1

Next, combine like terms:

– 2
`x^3` + 5
`x^3`+ 3
`x^2` – 2
`x^2` – 1

This simplifies to:

3
`x^3` +
`x^2` – 1

Now we have the final answer in standard form, where terms are arranged in descending order of their exponents.