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Hi can someone help me understand what Identity is in Basic Algebra please? watch

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Size:  57.7 KBHi I don't really understand what an Identity is and how it is from an equation?

    How do you get (x + 1)^2 ≡ x^2 + 2x + 1

    and when we do differences of square does that come into identity? And should we do foil with the outcome of differences of squares? so for example:

    4x^2 - 25
    = 4x^2 - 5^2
    = (4x-5)(4x+5)
    so do I do foil from here? and if I do, I get 16x^2 - 25 (but how is that identical to 4x^2 - 25)??

    Also can someone help me understand what the picture below is speaking about?

    Many thanks for your help.
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    4x2 - 25 is the difference of two squares... ( 2x - 5 )( 2x + 5 )
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    (Original post by transient life)
    Hi I don't really understand what an Identity is and how it is from an equation?
    As said in the description, an identity is when two expression are exactly the same for all values of x.

    A simple example would be:

    \displaystyle (x+1)^2 \equiv x^2+2x+1

    \displaystyle (x+1)^2 = \frac{(x+1)^3}{(x+1)}

    as you can see, the first equation is true for ALL values of x.

    However the second one is not an identity because it is NOT true for all values of x - namely for x=-1 as then the RHS is undetermined. Otherwise, every other value is exactly the same as you would get from the LHS.

    How do you get (x + 1)^2 ≡ x^2 + 2x + 1
    By expanding the brackets. (x + 1)^2 \equiv (x+1)(x+1)

    and when we do differences of square does that come into identity? And should we do foil with the outcome of differences of squares? so for example:

    4x^2 - 25
    = 4x^2 - 5^2
    = (4x-5)(4x+5)
    so do I do foil from here? and if I do, I get 16x^2 - 25 (but how is that identical to 4x^2 - 25)??
    Quite simply because it is NOT identical to 4x^2-25 as you've expanded wrong.

    a^2-b^2 \equiv (a+b)(a-b) \Rightarrow 4x^2-25\equiv (2x)^2-(5)^2\equiv (2x-5)(2x+5)

    Also can someone help me understand what the picture below is speaking about?

    Many thanks for your help.
    What picture? Do you mean the one above? It's simply explaining what an identity is.
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    (Original post by RDKGames)
    As said in the description, an identity is when two expression are exactly the same for all values of x.

    A simple example would be:

    \displaystyle (x+1)^2 \equiv x^2+2x+1

    \displaystyle (x+1)^2 = \frac{(x+1)^3}{(x+1)}

    as you can see, the first equation is true for ALL values of x.

    However the second one is not an identity because it is NOT true for all values of x - namely for x=-1 as then the RHS is undetermined. Otherwise, every other value is exactly the same as you would get from the LHS.



    By expanding the brackets. (x + 1)^2 \equiv (x+1)(x+1)



    Quite simply because it is NOT identical to 4x^2-25 as you've expanded wrong.

    a^2-b^2 \equiv (a+b)(a-b) \Rightarrow 4x^2-25\equiv (2x)^2-(5)^2\equiv (2x-5)(2x+5)



    What picture? Do you mean the one above? It's simply explaining what an identity is.
    Thank youu soo much!

    I'm reeaally bad at math and hate it, but I've got to study it for the uni course I want to be doing. I'm self taught so this helps a lot - thanks!
 
 
 
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