Factoring Perfect squares & GCF

Factoring – GCF and Perfect Squares

By: Abenai Chatman and Rosalba Urena


On our math project we are working on the topic Factoring – GCF and Perfect Squares. Anytime you have the difference of two perfect squares, you’ll always have two binomials. One of the binomial terms has to have a negative sign in between. You should always check your work so that you could see if you got your answer is right because sometimes you can get confused with the negative and positive signs. To find the GCF of a polynomial, trinomial, or a binomial you have to look an each term and determine if all the terms in the expression have the same variable and/or number. If the expression does, then you take out the variable and/or number and put the other terms in side the parenthesis.

Example Problems:

1. 25x² – 36

= (5x-6)(5x+6)
= 25x² + 30x – 30x – 36
= 25x² - 36

2. t² -25

= (t+5)(t-5)
= t² - 5t + 5t - 25
= t² - 25


3. y² - 36

= (y+6)(y-6)
= y² - 6y + 6y - 36
= y² - 36

4. 63yr² - 28y
= 7y (9r²- 4)
= 7y (3r - 2)(3r + 2)
= 7y (9r² + 6r – 6r – 4)
= 7y (9r² - 4)
= 63yr² - 28y

5. x² + 14x + 40
= (x + 10)(x + 4)
= x² + 4x + 10x + 40
= x² + 14x + 40


Independent Problems:


GCF:

1. 4x + 10x

2. 10xy² – 5x

3. 9ym² + 9ym

4. 25x² + 5x

5. 18ym² + 45yx


Factoring Perfect Squares:

6. p² + 16p + 63

7. s² + 12s + 20

8. h² - 14h + 48

9. w² + 13x + 30

10. y² - 13y – 36

In my conclusion through the expressions that come before this we can recognize that when we are factoring these perfect square binomials we are Factoring the Difference of Two Perfect Squares. Such as the example y²-36 we understand from knowing that they are both perfect squares that the answer is going to be (y - 6)(y + 6) because y · y = y² and the other perfect square 36 = 6 · 6. What these two Perfect Squares have in common is that they both when factored pull out twins of that same number instead of a different number. We learned that through factoring perfect squares that are binomials you must always have a subtraction sign for the expression.