Binomial Squares and Perfect Square Trinomials:

In the last lesson we learned about a special case of multiplying binomials called D.O.T.S.. In this case, the center terms always drop out leaving you with just a "difference of two squares" or D.O.T.S..

Well now, in this lesson we learn about yet another special case of multiplying binomials. In this case the original binomials are EXACTLY THE SAME, and when we multiply them, the outside and inside or "center" terms don't drop out, they DOUBLE.

Here take a quick look:

Watch what happens here if the binomials hold subtraction signs:

Try a couple yourself:

So now let's go the other direction. If we START with a perfect square trinomial and FACTOR it, we will get the binomial square that generated it.

Here let's look at one:

If this is a perfect square trinomial, it came from a binomial being squared. So go ahead and set up two sets of parentheses.

(......)(.......)

Now decide what the signs should be. If the center term on the trinomial is negative, the signs will both be negative. If the center term is positive the signs will both be positive.

(...-...)(...-...)

To fill in the remaining spots, just take the square roots of the first and last terms of the trinomial.

Now fill in the spots of the binomials and simplify to exponent form.

Give these a shot:

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