Verified answer

It is (x+1)(x+1) or (x+1)^2

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x² + 2x + 1 = ( x + 1 ) ( x + 1 ) = ( x + 1 ) ²

x² + 2x + 1

= (x + 1)²

What are two numbers that multiply to be 1, but add to be 2?

Hint:

1 × 1 = 1

1 + 1 = 2

So it's pretty obvious how to factor this:

(x + 1)(x + 1)

But those terms are the same, so you can just write the binomial once, but squared.

Answer:

(x + 1)²

P.S. Learn to recognize the squared binomial:

(a + b)² = a² + 2ab + b²

In your case, the first and last terms are squares:

x² = x * x

1 = 1 * 1

And the middle term is double the product:

2 * x * 1 = 2x

So just by recognizing the form, you should be able to directly see that's a squared binomial.

x² + 2x + 1

= (x + 1)²

x^2 + 2x + 1 =

(x + 1)^2

x^2 + 2x + 1

= (x + 1)^2

(x+1)^2 .... ... . . . .