Simplify (8x² - 1 + 2x³) - (7x³ - 3x² + 1).

Solution:

Given difference between polynomials (8x² - 1 + 2x³) - (7x³ - 3x² + 1)

A polynomial is defined as an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s)

In order to perform the difference, we need to club together the terms with same exponents of the variable.

So re-write (8x² - 1 + 2x³) - (7x³ - 3x² + 1) as follows

(2x³ - 7x³) + (8x² - (-3x²) + (-1 - (1))

Here, the terms of degree 3 are put together, of degree 2 are put together and constants are put together for easy operation

Now, take the common term from them and perform the difference

x³(2 - 7) + x²(8 + 3) + (-1 - 1)

-5x³ + 11x² - 2

The difference is given by -5x³ + 11x2 - 2