(x+4)(x+2) In Expanded Form

Jasonbradley

2 min read

·

Jun 16, 2024

27

Share

Expanding (x+4)(x+2)

In mathematics, expanding an expression means rewriting it in a simpler form, typically by removing parentheses. In this case, we have the product of two binomials: (x+4)(x+2).

Using the FOIL Method

The FOIL method is a common way to expand binomials. It stands for First, Outer, Inner, Last, which represents the order in which we multiply the terms:

1. First: Multiply the first terms of each binomial: x * x = x²
2. Outer: Multiply the outer terms: x * 2 = 2x
3. Inner: Multiply the inner terms: 4 * x = 4x
4. Last: Multiply the last terms: 4 * 2 = 8

Now, we add all the results together:

x² + 2x + 4x + 8

Finally, we combine the like terms:

x² + 6x + 8

Therefore, the expanded form of (x+4)(x+2) is x² + 6x + 8.

Alternative Method: Distributive Property

Another approach is using the distributive property. We can distribute the first binomial (x+4) over the terms of the second binomial (x+2):

(x+4)(x+2) = x(x+2) + 4(x+2)

Then, we distribute again:

= x² + 2x + 4x + 8

Combining like terms, we get the same result:

x² + 6x + 8

Both methods lead to the same expanded form, demonstrating that you can choose the approach you find easiest and most comfortable.