Q1: How can you tell if a trinomial is a perfect square, without factoring?
Give at least two examples of a trinomial square in standard and factored forms
You must use variables and numbers in each example.
The expressions a 2 + 2ab + b2 and a 2 − 2ab + b2 are called perfect square trinomials.
If we can recognize a perfect square trinomial, we can use the following formulas to
factor it:
a 2 + 2ab + b2 = (a + b)
and
a 2 − 2ab + b2 = (a − b)2
When factoring a trinomial as a perfect square trinomial, we must first verify that the
middle term is correct. Here are some examples:
x 2 + 10x + 25 = (x + 5)2
4 y 2 − 4 y + 1 = (2 y − 1)2
x 2 + 4xy + 4 y 2 = (x + 2 y)2
Q2:. How can you tell if a polynomial is a difference of two squares without factoring?
Give at least two examples of a difference of squares polynomial in standard and factored
forms. You must use variables and numbers in each example.
The difference of two squares can be factored as follows: a 2 − b2 = (a − b)(a + b) . So if
we are given an expression that is the difference of two terms, and each is a perfect
square, we can immediately factor it into this form. Here are some examples:
4x 2 − 9 = (2x − 3)(2x + 3)
100 − 16t 2 = (10 − 4t)(10 + 4t)
49 y 2 − 64z 2 = (7 y − 8z)(7 y + 8z)