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