Final answer:
To factor x^2+4x+4 with algebra tiles, represent the expression with tiles and arrange them into a perfect square, showing that it factors into (x+2)^2 which is a perfect square trinomial.
Step-by-step explanation:
To factor the quadratic expression x^2+4x+4 using algebra tiles, you would visually represent the terms with tiles and arrange them into a perfect square. The term x^2 would typically be represented by a large square tile, the term 4x by four rectangular tiles (each representing x), and the constant term 4 by four small square tiles, each representing the number 1.
When you arrange these tiles to form a larger square, the side length of this large square will be composed of the x tile and two unit tiles, since the large square must account for all terms in the expression. Therefore, this arrangement shows that x^2+4x+4 factors into (x+2)(x+2), or more simply, (x+2)^2. This is a perfect square trinomial, which means that the quadratic you're factoring is the square of a binomial.