(5n-5)(2+2n) In Standard Form

2 min read Jun 16, 2024

Expanding and Simplifying (5n-5)(2+2n)

This article will demonstrate how to expand and simplify the expression (5n-5)(2+2n) into standard form.

Understanding Standard Form

Standard form for a polynomial refers to writing it in descending order of powers of the variable, with each term separated by a plus or minus sign. For example, a quadratic expression in standard form would look like ax² + bx + c.

Expanding the Expression

To expand the given expression, we can use the FOIL method, which stands for:

First: Multiply the first terms of each binomial.
Outer: Multiply the outer terms of the binomials.
Inner: Multiply the inner terms of the binomials.
Last: Multiply the last terms of each binomial.

Applying this to our expression:

First: (5n) * (2) = 10n
Outer: (5n) * (2n) = 10n²
Inner: (-5) * (2) = -10
Last: (-5) * (2n) = -10n

Now we have: 10n + 10n² - 10 - 10n

Simplifying the Expression

To simplify, we combine like terms:

10n² + (10n - 10n) - 10

This results in: 10n² - 10

The Final Answer

Therefore, the expression (5n-5)(2+2n) in standard form is 10n² - 10.