Math 1 Difference Of Two Squares Homework In Spanish

Interestingly, you can do this one logically just as well and as easily as Grigori's mathematical method (it is, in fact, the same thing, just in a different idiom):

 

The square root is defined as the number which, when multiplied by itself, gives the number in question (x in this problem).  In most cases, the number in question will be a positive one.  All positive numbers have two square roots, one positive and one negative.  This is because multiplying a positive by a positive results in a positive and multiplying a negative by a negative results in a negative.  Because the positivity/negativity of the roots, in a way doesn't matter, we can see that the absolute values of the two (that is, their value without regard to negativity/positivity) must be the same.  Thus, they must reflect around zero, each being an equal distance away from zero.  Thus, since we know the difference between the roots is 30, half of which is 15, we must therefore also know that the roots are going to be 15 and -15, so we can just go ahead and square that.

1) First check for common factors - there are none, so we can

continue on to check the criteria. It is a binomial with two perfect squares and subtraction, so we can use this pattern.


We set up two parenthesis with a+ in one and a- in the other
We take the square root of x2, which is x, and put that in the

front of each parenthesis. We take the square root of 25 which is 5 and put that in the back of each.

Final answer: . We can check this by multiplying it out (remember to
distribute or use FOIL). We get . This matches the original, so we know we factored correctly.



2) First check for common factors – there are none, so we can

continue on to check the criteria. It is a binomial with two perfect squares and subtraction, so we can use this pattern.


We set up two parenthesis with a+ in one and a- in the other
We take the square root of , which is , and put that

in the front of each parenthesis. We take the square root of 4x2 which is 2x and put that in the back of each.


Final answer. We can check this by multiplying it out
(remember to distribute or use FOIL). We get . This matches the original, so we know we factored correctly.


3) First we check for common factors. There is a common factor of 3, so we must factor that out first.
Now we look at . This meets the criteria for the pattern, so we can factor it using the pattern. Just bring down the 3 in front of theparenthesis.
Answer:
We can check this by multiplying everything out. Let's distribute the 3 first:


Practice: Factor the following. Check for common factors first then the difference of two squares.

1)

2)

3)

4)

5)

Answers: 1) 2) 3) 4) 5)

0 comments

Leave a Reply

Your email address will not be published. Required fields are marked *