How do you factor out perfect square trinomials?
To factor out perfect square trinomials, you need to follow the steps below:
Step 1: Identify the form of the trinomial. A perfect square trinomial can be written in the form of (ax + b)^2 or (ax - b)^2, where a and b are constants.
Step 2: Write down the square of the binomial. You need to square the first term and the last term of the binomial in the trinomial. For example, if the trinomial is 9x^2 + 12x + 4, you would square the first term (9x)^2 = 81x^2 and square the last term 4^2 = 16.
Step 3: Take the square root of the first and last terms you just found. In the same example, the square root of 81x^2 is 9x, and the square root of 16 is 4.
Step 4: Set up the factors. Using the square roots from the previous step, write down two sets of parentheses. In the example, it would be (9x + 4) and (9x + 4).
Step 5: Combine the terms. Inside the parentheses, write down the square root term with the appropriate sign. In the example, it would be (9x + 4)(9x + 4).
Step 6: Simplify the factors. Multiply the factors together, and you will have factored out the perfect square trinomial. In the example, it would be (9x + 4)(9x + 4) = (9x + 4)^2.
By following these steps, you can factor out perfect square trinomials.