Question

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

Answer 1

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.