(x+6)(x+2)

2 min read Jun 17, 2024

Expanding the Expression (x+6)(x+2)

In mathematics, expanding an expression means writing it in a simpler form without parentheses. Here's how to expand the expression (x+6)(x+2):

Using the FOIL Method

The FOIL method is a common technique for expanding binomials (expressions with two terms). It stands for First, Outer, Inner, Last. Here's how it works:

First: Multiply the first terms of each binomial: x * x = x²
Outer: Multiply the outer terms of the binomials: x * 2 = 2x
Inner: Multiply the inner terms of the binomials: 6 * x = 6x
Last: Multiply the last terms of each binomial: 6 * 2 = 12

Now, combine the terms: x² + 2x + 6x + 12

Finally, simplify by combining like terms: x² + 8x + 12

Therefore, the expanded form of (x+6)(x+2) is x² + 8x + 12.

Alternative Method - Distributive Property

You can also expand the expression using the distributive property. This method involves distributing each term of the first binomial over the second binomial:

x * (x+2) = x² + 2x
6 * (x+2) = 6x + 12

Now, combine the results from both steps: x² + 2x + 6x + 12

Finally, simplify by combining like terms: x² + 8x + 12

Conclusion

Both the FOIL method and the distributive property lead to the same simplified form: x² + 8x + 12. Choose whichever method you find easier and more comfortable to apply.