Factoring Trinomial squares: 144-(p-8)^2

[Leipart]

144-(p-8)^2

Please help....exam tomorrow!!!!!
Could you please break it down, because I know the answer just not hot to get that answer.
(20-P) (4 + P)

 

[stapel]

144-(p-8)^2

Hint: Review the rule for factoring differences of squares. (And, if you haven't memorized that rule already, do it now!)

Eliz.

 

[Leipart]

I know that rule already ex. A^2 - B^2 = (A+B) (A-B), but that doesn't help me make sense of this problem

 

[Leipart]

Please help solve 144-(p-8)^2

I understand that (p-8)(p+8) but what happenswith the 144

 

[o_O]

Re: Please help solve 144-(p-8)^2

What are you solving for? Do you mean factor?

Well, doesn't this look suspiciously like an application of the difference of squares?

\(\displaystyle a^{2} - b^{2} = (a+b)(a-b)\)

Now imagine a[sup:1gpy2ibo]2[/sup:1gpy2ibo] = 12[sup:1gpy2ibo]2[/sup:1gpy2ibo] and b[sup:1gpy2ibo]2[/sup:1gpy2ibo] = (p - 8)[sup:1gpy2ibo]2[/sup:1gpy2ibo]

:wink:

 

[stapel]

I know that rule...but that doesn't help me make sense of this problem

Since the expression is a difference of squares, the "difference of squares" formula should be helpful, shouldn't it...? :wink:

Eliz.

 

[Leipart]

I still dont understand...am I supposed to get (144p-8)(144p+8) but what do I do after that?

Since the expression is a difference of squares, the "difference of squares" formula should be helpful, shouldn't it...?

It should be but its not, I dont understand what happens with the 144...how to get the answer of (20+p)(4-p)

 

[stapel]

Re: Please help solve 144-(p-8)^2

am I supposed to get (144p-8)(144p+8)...?

Please reply showing the steps you used, starting with the "difference of squares" formula I'd suggested, and showing how you plugged the "a" and "b" that were given to you by .

Thank you!

Eliz.

 

[o_O]

Sorry I made a typo:
Imagine a[sup:1pmsix2p]2[/sup:1pmsix2p] = 144 and b[sup:1pmsix2p]2[/sup:1pmsix2p] = (p - 8)[sup:1pmsix2p]2[/sup:1pmsix2p]

Your problem IS a difference of squares problem. Just apply the above and see what you get.

 

[Leipart]

a^2+B^2=(a+b)(a-b)

144-(p-8)^2
(12p+8)(12p-8)...ok now how do I get (20+p)(4-p)

 

[stapel]

a^2+B^2=(a+b)(a-b)

No: a[sup:1cz04xkb]2[/sup:1cz04xkb] - b[sup:1cz04xkb]2[/sup:1cz04xkb] = (a + b)(a - b). The variables should match, and you should being with a difference (especially since the sum of squares is not factorable). As suggested earlier, it would be good to review and memorize this formula.

144-(p-8)^2

If 12[sup:1cz04xkb]2[/sup:1cz04xkb] - (p - 8)[sup:1cz04xkb]2[/sup:1cz04xkb] = a[sup:1cz04xkb]2[/sup:1cz04xkb] - b[sup:1cz04xkb]2[/sup:1cz04xkb], then what does each of "a" and "b" equal?

(12p+8)(12p-8)...ok now how do I get (20+p)(4-p)

You cannot the correct answer from your work. You first need to apply the values you've been given for "a" and "b", and insert them into the formula you've been given. To clarify:

You've been given the expression 144 - (p - 8)[sup:1cz04xkb]2[/sup:1cz04xkb].

You've been told that 144 = 12[sup:1cz04xkb]2[/sup:1cz04xkb], so the expression may also be written as 12[sup:1cz04xkb]2[/sup:1cz04xkb] - (p - 8)[sup:1cz04xkb]2[/sup:1cz04xkb].

You've been told that this really is a difference of squares: 144 is 12 squared and (p - 8)[sup:1cz04xkb]2[/sup:1cz04xkb] is p - 8 squared, and subtraction is a "difference".

You've been told to use the formula "a[sup:1cz04xkb]2[/sup:1cz04xkb] - b[sup:1cz04xkb]2[/sup:1cz04xkb] = (a + b)(a - b)".

You've been told to compare "12[sup:1cz04xkb]2[/sup:1cz04xkb] - (p - 8)[sup:1cz04xkb]2[/sup:1cz04xkb]" with "a[sup:1cz04xkb]2[/sup:1cz04xkb] - b[sup:1cz04xkb]2[/sup:1cz04xkb]" to figure out what "a" and "b" should be.

You've been told that a[sup:1cz04xkb]2[/sup:1cz04xkb] = 12[sup:1cz04xkb]2[/sup:1cz04xkb] and that b[sup:1cz04xkb]2[/sup:1cz04xkb] = (p - 8)[sup:1cz04xkb]2[/sup:1cz04xkb], meaning that a = 12 and b = (p - 8).

You've been told to plug the given values of "a" and "b" into the given formula, and to simplify to obtain the given solution.

Please reply showing what you did (all of your steps), so we can try to figure out how you are getting "(12p + 8)(12p - 8)" from what you've been given. Thank you.

Eliz.

 

[Leipart]

Would you times the problem by negative 1, because there is a negative after the 144

 

[Leipart]

so I got (12+p+8)(12-p-8) how do I get them to equal 20 and 4

 

[Denis]

so I got (12+p+8)(12-p-8) how do I get them to equal 20 and 4

Just simplify what's inside each set of brackets, then STOP!

 

[stapel]

Would you times the problem by negative 1, because there is a negative after the 144

What...? The above makes it sound like you aren't familiar with the "difference of squares" formula, since you don't understand that "difference" means "subtraction" and that the formula only applies if there is a "minus" between the squares. So please first study and learn about what this formula is and how it works:

. . . . .Google results for "difference of squares"

so I got (12+p+8)(12-p-8) how do I get them to equal 20 and 4

As has been pointed out earlier, we cannot check work that we cannot see. Providing only an incorrect final result does not allow us to trouble-shoot and figure out which part of the step-by-step instructions you aren't following. Please reply with that information:

You've been given the expression 144 - (p - 8)[sup:16kt6tgv]2[/sup:16kt6tgv].

You've been told that 144 = 12[sup:16kt6tgv]2[/sup:16kt6tgv], so the expression may also be written as 122 - (p - 8)[sup:16kt6tgv]2[/sup:16kt6tgv].

You've been told that this really is a difference of squares: 144 is 12 squared and (p - 8)[sup:16kt6tgv]2[/sup:16kt6tgv] is p - 8 squared, and subtraction is a "difference".

You've been told to use the formula "a[sup:16kt6tgv]2[/sup:16kt6tgv] - b[sup:16kt6tgv]2[/sup:16kt6tgv] = (a + b)(a - b)".

You've been told to compare "12[sup:16kt6tgv]2[/sup:16kt6tgv] - (p - 8)[sup:16kt6tgv]2[/sup:16kt6tgv]" with "a[sup:16kt6tgv]2[/sup:16kt6tgv] - b[sup:16kt6tgv]2[/sup:16kt6tgv]" to figure out what "a" and "b" should be.

You've been told that a[sup:16kt6tgv]2[/sup:16kt6tgv] = 12[sup:16kt6tgv]2[/sup:16kt6tgv] and that b[sup:16kt6tgv]2[/sup:16kt6tgv] = (p - 8)[sup:16kt6tgv]2[/sup:16kt6tgv], meaning that a = 12 and b = (p - 8).

You've been told to plug the given values of "a" and "b" into the given formula, and to simplify to obtain the given solution.

Please reply showing what you did (all of your steps)....

Thank you.

Eliz.