decide whether each trinomial is a perfect square. if so, factor it.
x^2 - 4x + 4
how do i solve this?? i don't understand the method..
is it (x - 2x)^2 ?
(x - 2x)^2
Expand:
(x - 2x)(x - 2x)
Simplify using the Foil Method:
http://www.algebrahelp.com/lessons/simplifying/foilmethod/pg2.htm
does it equal to x^2 - 4x + 4 ?
To determine whether the trinomial x^2 - 4x + 4 is a perfect square, we can use a simple method.
Step 1: Check the first and last terms. In this case, the first term is x^2 and the last term is 4.
Step 2: Take the square root of the first term and the square root of the last term. Here, the square root of x^2 is x, and the square root of 4 is 2.
Step 3: Multiply the square root of the first term and the square root of the last term. In this case, x * 2 = 2x.
Step 4: Now, check if the middle term (-4x) matches the product from step 3 (2x). If they are equal, then the trinomial is a perfect square.
In this case, since -4x does indeed match 2x, the trinomial x^2 - 4x + 4 is a perfect square.
To factor a perfect square trinomial, we can simply take the square root of the first and last terms and rewrite it as (x - 2)^2.
Therefore, the factored form of the trinomial x^2 - 4x + 4 is (x - 2)^2.