Question

Does this make sense? Is my answer correct?

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.

The sum of two squares can be: (a^2 + b^2)
The difference of two squares can be:(a^2 - b^2)

The difference is that the difference of two squares can be factored to (a - b)(a + b). The sum of two squares cannot be factored like this.

Answer 1

difference of two squares example:
4x2−25=(2x)2−(5)2=(2x−5)(2x+5)

sum of two squares example:
4x2+25=(2x)2+(5)2=(2x−5a)(2x+5a)

Answer 2

This mite make the examples easier to read:

Difference of two squares example:
4x^2 − 25 =(2x)^2 − (5)^2 =(2x - 5)(2x + 5)

Sum of two squares example:
4x^2 + 25 =(2x)^2 +(5)^2 =(2x − 5a)(2x + 5a)

Answer 3

Find the product: (x + 5)(x – 5)

x2 + 25
x2 − 25<----- My Answer
x2 − 10
3x2 + 8x − 3y

2. Factor Completely: x2 − 36

(x + 6)(x – 6)<---- My Answer
(x + 6)(x + 6)
(x – 6)(x − 6)
Prime

3. Factor Completely: 4x2 − 81

(4x – 9)(x + 9)
(2x + 9)(2x + 9)
(2x + 9)(2x – 9)<---- My Answer
(2x – 9)(2x − 9)

4. Factor Completely: x2 + 16

(x + 4)(x + 4)
(x + 4)(x – 4)
Prime<---- My Answer
(x – 4)(x − 4)

5. Factor Completely: 2x2 − 18

Prime
2(x2 − 9)
2(x + 3)(x – 3)<--- My Answer
2(x + 3)(x + 3)

6. Factor Completely: 3x2 − 21

3(x2 − 7)<---- My Answer
3(x + 7)(x – 7)
3(x + 7)(x – 3)
Prime

Answer 4

"links" dont blue up in the fan testimonials; if anything you can get someones attention best by pinging them:

@amistre64 @Renee99

Answer 5

The essay part is the one I'm most worried about, does that one look good? or bad?

Answer 6

ohh, sorry I didn't know...

Answer 7

these answers look fine; i cant see an "essay" part .... im old and theres just alot of visual noise going on in this post :)

Answer 8

okay, sorry about that... here is my answer to the essay again... sorry about the confusion!

The sum of two squares can be: (a^2 + b^2)
The difference of two squares can be:(a^2 - b^2)

The difference is that the difference of two squares can be factored to (a - b)(a + b). The sum of two squares cannot be factored like this.

Difference of two squares example:
4x^2 − 25 =(2x)^2 − (5)^2 =(2x - 5)(2x + 5)

Sum of two squares example:
4x^2 + 25 =(2x)^2 +(5)^2 =(2x − 5a)(2x + 5a)

Answer 9

I agree that the answers look good.

Hey amistre, that ping that you mentioned, does that cause a notification to go out to the person being pinged?

Answer 10

Sum of two squares example:
4x^2 + 25 =(2x)^2 +(5)^2 [Not=] (2x − 5a)(2x + 5a)

im not to sure how technical they need to be, since the sum of 2 squares is factorable by complex numbers

Answer 11

yes @ChrisS

Answer 12

Cool. That's good to know.

Answer 13

ohh, so I just need to take out the = sign in this:4x^2 + 25 = (2x)^2 +(5)^2 = (2x − 5a)(2x + 5a)

and turn it into this: 4x^2 + 25 = (2x)^2 +(5)^2 (2x − 5a)(2x + 5a)

Answer 14

\[\ne \]
there really isnt a good ascii symbol unless you can find an "alt" combo for it :)

♫☼W/►

Answer 15

what is that? Iv'e never used that sign before?

Answer 16

its the equals sign thats been scratched out;

it means not equal to

Answer 17

I can't make that sign on the computer, should I just not put a sign at all?

Answer 18

use words :) just type in: [not equal to]

Answer 19

of course im not sure how your essay is formatted for your submission

Answer 20

okay! that will work, thanks! and its just a regular rich text document.

Answer 21

the sum of 2 squares cannot be factored across the Reals.

x^2 + a^2 = 0

x^2 = - a^2

x = sqrt(-a)

Answer 22

If you have Word, there is an equation editor built in to it that has most mathematical symbols including the "not equal to" symbol.

Answer 23

Should I just add that into my answer?

Answer 24

Like this? :The sum of two squares can be: (a^2 + b^2)
The difference of two squares can be:(a^2 - b^2)

the sum of 2 squares cannot be factored across the Reals.

x^2 + a^2 = 0

x^2 = - a^2

x = sqrt(-a)

The difference is that the difference of two squares can be factored to (a - b)(a + b). The sum of two squares cannot be factored like this.

Difference of two squares example:
4x^2 − 25 = (2x)^2 − (5)^2 = (2x - 5)(2x + 5)

Sum of two squares example:
4x^2 + 25 = (2x)^2 +(5)^2 [not equal to](2x − 5a)(2x + 5a)

Answer 25

:) im not sure how technical your question needs to be. If you have not covered material relating Reals and Complexes then its prolly best to avoid it.

Answer 26

yeah, i'm not on that yet, so I won't mention it... Thanks again for all of your help!! :)