Subject: Completing the Square.

Lexa Michaels.
secondary. student.

the question: how do you complete a square? the textbook question is: x 4 + 64

Hi Lexa,

Completing a square involves seeing a pattern in an algebraic expression. The pattern is on the right hand side of the expression

(y + a) 2 = y 2 + 2a y + a 2

The pattern I see is in the relationship between the coefficient of y, 2a, and the constant term a 2. To make this match your expression first y = x 2 so that y 2 = (x 2) 2 = x 4. Second you have a 2 = 64 so a = 8 and hence 2a = 16. Thus to complete the square with x 4 + 64, add 16 x 2 to get

x 4 + 16 x 2 + 64 = (x 2 + 8) 2
Cheers,
Penny
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