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The sum of two numbers a and b  is 20. Write an expression for the sum of their squares, in terms of a.

 Dec 5, 2021
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The sum of two numbers a and b  is 20. Write an expression for the sum of their squares, in terms of a.  

 

Okay, so we want a2 + b2 but we want it in terms of a only.  We can do that. 

 

Since a + b = 20, that means that b = 20 – a.         So, we'll just substitute it in.  

 

a2 + b2  =                        a2 + (20 – a)2                  Next, multiply out that second term.  

 

a2 + (20 – a)2  =              a2 + (400 – 40a + a2)      Then, combine like terms.  

 

a2 + (400 – 40a + a2)  =  2a2 – 40a + 400              The 2 will come out of that  

 

2a2 – 40a + 400  =           2 • (a2 – 20a + 200)         I think that's about as far as it will reduce. 

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 Dec 5, 2021

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