Question

Create a unique perfect square trinomial using what you know about the characteristics of a perfect square trinomial. Explain why the trinomial you created is considered a perfect square trinomial.

Part 2: Using complete sentences, explain how to factor the trinomial you created and provide the factors.

Answer 1

a perfect square trinomial is one that factors into two identical factors

Example: (2x+5)(2x+5)=(2x+5)^2=4x^2+20x+25

the left and middle are factored form of the perfect square trinomial on the right side above)

Answer 2

part 2
when you start with the trinomial 4x^2+20x+25, notice that the first and last terms are perfect squares; take their square roots to get 2x and 5, now consider the product 2*2x*5 which equals the middle term of the trinomial, right?
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Answer 3

when you square a binomial you get\[(a+b)^2=a^2+2ab+b^2\]in our example a=2x and b=5, and the middle term is 2ab or 2*2x*5. that's how you identify the perfect square trinomial when you want to factor one; then you know that it factors to a product of the same binomial each of the form a-b.
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Answer 4

Example: factor 4x^2+20x+25

relative to the above formula, a=2x and b=5 and so\[4x^2+20x+25=(2x+5)(2x+5)=(2x+5)^2\]
Questions?

Answer 5

Using complete sentences, compare and contrast the ways to factor the "sum of two squares" and the "difference of two squares." Provide an explanation and example of each, including any similarities and differences