Abigail S.

asked • 02/27/24

Fill in the blank with a number to make the expression a perfect square.

y2-2y+

Brenda D.

tutor
Hi Abigail S, since you have this labeled under Geometry I was just wondering if you’ve completed Algebra? My reason for asking is because there is a method called Completing the Square that could apply to your question. It goes like this see x2 + bx can be rearranged nearly into a square ... So, by adding (b/2)^2we can complete the square. The result of (x+b/2)^2 has x only once, which is easier to use. Your question has y as the variable instead of X. Your question has y^2 - by +. instead and b= -2.
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02/27/24

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Joanne C. answered • 02/27/24

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Hi Abigail...


Your Question: Fill in the blank with a number to make the expression a perfect square.

y2-2y+


The perfect square would be (y+b/2)2

If you multiply it out it would be (y+b/2)(y+b/2) = y2+by + (b/2)2

Your equation y2-2y look at the -2y and look at the +by above.

Set the coefficient of you equation equal to the coefficient of the 2nd term in the other equation

-2 = b

To get a perfect square you need to add (b/2)2 to your equation b=-2 so you add (-2/2)2= 1

y2-2y+1 This would then be factored into (y-1)(y-1)


Then general way that you figure out the perfect square is

1) Make sure y2term has a coefficient of 1

2) take the coefficient of the y term , divide by 2 this will equal your b/2 term

3) add (b/2)2 to your equation

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