Simplified Form and Factorization of the Expression x^2 + 8x + 16

x^2 + 8x + 16

The given expression is x^2 + 8x + 16

The given expression is x^2 + 8x + 16.

To understand this expression, let’s break it down into its individual terms:

Term 1: x^2
This term represents the square of the variable x, which means multiplying x by itself.

Term 2: 8x
This term represents the product of 8 multiplied by x, where x is the variable.

Term 3: 16
This is a constant term, having the value 16, which means it does not contain any variables.

Now, to simplify the expression, we can try to factorize it.

The first term x^2 could be factored as (x)(x) or (x)^2.

The last term 16 could be factored as (4)(4) or (4)^2.

Now we need to find the factors of 16 that, when combined together, will yield the middle term 8x. The factors of 16 are 1 and 16, 2 and 8, and 4 and 4. Among these, the factor pair that stands out is 4 and 4, because they add up to give us 8.

So, the expression can be factored as follows:
(x + 4)(x + 4)

Notice that we have (x + 4) repeated twice, which can be written more simply as:
(x + 4)^2

Therefore, the fully factored form of the expression x^2 + 8x + 16 is (x + 4)^2.

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