Question

Pick a two-digit number greater than 25. Rewrite your two-digit number as a difference of two numbers. Show how to use the identity (x − y)2 = x2 − 2xy + y2 to square your number without using a calculator.
I picked 26 30-4=26
division 26^2=(30-4)^2= 30^4*2*30-4+4^2

My teacher told me I need to FOIL. Which I don't understand what to do.. IF you could show me how with steps that would be great.

Answer 1

The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which occur first in each binomial. Then Outer means multiply the outermost terms in the product. Inner means multiply the innermost two terms. Last means multiply the terms which occur last in each binomial. Then simplify the products and combine any like terms which may occur.

Answer 2

@drumminboy918 So could you help me with that, Which equation do I use FOIL on?

Answer 3

26^2=(30-4)^2= 30^4*2*30-4+4^2

This is the Equation you use it on

Answer 4

@drumminboy918 What about 30^4*2*30-4+4^2 the -4+4^2, do I not worry about it and just do 30^4*2*30 using foil

Answer 5

You use it on both sides of the equation I told you to do

Answer 6

@drumminboy918 I don't understand, how do I multiply 26^2=(30-4)^2, can you help me

Answer 7

Here I'll give you a example

Answer 8

Example: (x + 2)(x + 5) = x·x + x·5 + 2·x + 2·5
First Outer Inner Last

= x2 + 7x + 10

Answer 9

ok

Answer 10

Do the same thing here

26^2=(30-4)^2= 30^4*2*30-4+4^2

Answer 11

What did you multiply to get x2+7x+10 in the example

Answer 12

I am just simplifying the left side

Answer 13

Can you give me the part of my equation to simplify for the first part of FOIL

Answer 14

I man right

Answer 15

sorry

Answer 16

mean* gosh I cant type today

Answer 17

so 4^2 is my right side do I simply that

Answer 18

simplify

Answer 19

yes

Answer 20

So 16 is the answer for F, then we move on to O?

Answer 21

First, Outer, Inner, Last

Answer 22

Your getting the hang of it

Answer 23

Wouldn't the outermost be the right side to?

Answer 24

The outer of the right side

Answer 25

I just did that?

Answer 26

all your doing is simplifying

Answer 27

that's all FOIL is

Answer 28

A fancy way of simplifying

Answer 29

So can you tell me what part I neeed to simplify for O now? as 4^2 is the outtermost

Answer 30

Sadly I cant do this for you, but what ive seen so far, you can do this. But this place is easy simple and fun

http://www.algebrahelp.com/lessons/simplifying/foilmethod/

Answer 31

@drumminboy918 but is what I got for the first part right? I'm not asking for the answers just what you are telling me is going against what you told me above.

Answer 32

Im not sure, that why. I use this link all the time

Answer 33

@drumminboy918 Yeh, i'm looking at the site, so 16 is not correct.. I don't understand how I use foil on this if I don't have 2 sets of parentheses

Answer 34

You need 2 sets of parentheses. Choose a different equation with a set of 2 parentheses.

Answer 35

@Klip My teacher told me the equation was right for this and that I just needed to foil, so what I did was I did this 26^2=(30-4)^2= 30^4*2*30-(4+4)^2. Then I foiled

Answer 36

@Klip So that would work? Thanks