Question

Fill in the blank with a number to make the expression a perfect square.
u^2+8u+?

Answer 1

16

Explanation:

Hello, do you remember that result?

For any a and b real numbers,

`(a+b)^2=a+2\cdot a \cdot b+b^2`

In this example, we have.

`u^2+8u=u^2+2\cdot 4 \cdot u\\\\\text{ This is the beginning of ... } u^2+8u+4^2=u^2+8u+16\\\\\text{ So, we need to add 16 to make a perfect square}\\\\u^2+8u+\boxed{16}=u^2+2\cdot 4\cdot u +4^2=(u+4)^2`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you