Distributive Property

[ILovePizza]

I have a 3-part question; the first, I think I have, but need confirmation:

(1) Use the distributive property to calculate 56^2 and 48^2

56^2 = (56)(56)
____ = (50 + 6) (50 + 6)
____ = 2500 + 100n + n^2
____ = 2500 + 600 + 36
____ = 3136
--------------------------------------
48^2 = (48)(48)
____ = (40 + 8) (40 + 8)
____ = 2500 + 100n + n^2
____ = 2500 – 200 + 4
____ = 2304
--------------------------------------
I’m not exactly sure what or how to address the next 2 questions.

(2) Explain how to calculate the square of a number that is x units away from 50.

7^2 (49) ????

(3) Test this method using whole numbers close to 20. Does the pattern work for any value or only for values close to 50? Explain.

4^2 (16) ????

I’m not sure what’s required: I can’t go higher than 4, as 5 * 5 = 25

All help appreciated.

 

[Deleted member 4993]

I have a 3-part question; the first, I think I have, but need confirmation:

(1) Use the distributive property to calculate 56^2 and 48^2

56^2 = (56)(56)
____ = (50 + 6) (50 + 6)
____ = 2500 + 100n + n^2
____ = 2500 + 600 + 36
____ = 3136
--------------------------------------
48^2 = (48)(48)
____ = (40 + 8) (40 + 8)..................(50-2)^2 = 2500 - 100*2 +2^2
____ = 2500 + 100n + n^2
____ = 2500 – 200 + 4
____ = 2304
--------------------------------------
I’m not exactly sure what or how to address the next 2 questions.

(2) Explain how to calculate the square of a number that is x units away from 50.

\(\displaystyle (50 \, \pm \, x)^2 \, = \, 2500 \pm 100x + x^2\)


7^2 (49) ????

(3) Test this method using whole numbers close to 20. Does the pattern work for any value or only for values close to 50? Explain.

4^2 (16) ????

I’m not sure what’s required: I can’t go higher than 4, as 5 * 5 = 25

All help appreciated.

 

[ILovePizza]

OK, I see the correction in my logic for 48^2. I now understand that - thank you!

However, for question 2, I'm not so clear: (50 + x)^2 = 2500 + 100x + x^2 Hang on....thinking out-loud; OK, I think I understand. So 50 + x^2 (anything can be x)...I think I have this one to.

Now question 3, I'm still uncertain.

I do however, appreciate your help so far!