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Fill in the blank with a number to make the expression a perfect square. W^2 -8w +____

User Vidyanand
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1 Answer

2 votes

Solution:

Remember that a perfect square is a number (or expression), that can be expressed as the square of a number (or expression). For example,


a^2-2ab+b^2

is a perfect square, because it can be expressed as the square of the following expression:


(a-b)

that is:


(a-b)^2=a^2-2ab+b^2

now, in this case, notice that:


(w-4)^2=w^2-2(4)w+4^2

this is equivalent to:


=w^2-8w+4^2

or


=w^2-8w+16

thus, we can conclude that the missing space in the expression


w^2-8w\text{ + \_\_\_\_}

would be 16.

User Atisman
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