Simplify (3a⁴ - 2a² + 5a - 10) - (2a⁴ + 4a² + 5a - 2).

Solution:

Given, (3a⁴ - 2a² + 5a - 10) - (2a⁴ + 4a² + 5a - 2)

Now, 3a⁴ - 2a² + 5a - 10 - 2a⁴ - 4a² - 5a + 2

Grouping of common terms,

= 3a⁴ -2a⁴ - 2a² - 4a2 + 5a - 5a - 10 + 2

= a⁴ - 6a² - 8

Therefore, (3a⁴ - 2a² + 5a - 10) - (2a⁴ + 4a² + 5a - 2) = a⁴ - 6a² - 8.

Example:

Simplify (2a⁴ - a² + a - 11) - (4a⁴ + 4a2 + a - 2).

Solution:

Given, (2a⁴ - a² + a - 11) - (4a⁴ + 4a2 + a - 2)

Now, 2a⁴ - a² + a - 11 - 4a⁴ - 4a² - a + 2

Grouping of common terms,

= 2a⁴ - 4a⁴ - a² - 4a² + a - a - 11 + 2

= -2a⁴ - 5a² - 9

Therefore, (2a⁴ - a² + a - 11) - (4a⁴ + 4a² + a - 2) = -2a⁴ - 5a² - 9.

Simplify (3a⁴ - 2a² + 5a - 10) - (2a⁴ + 4a² + 5a - 2).

Summary:

(3a⁴ - 2a² + 5a - 10) - (2a⁴ + 4a² + 5a - 2) is a⁴ - 6a² - 8.