Question

Which of the following values "completes the square," or creates a perfect square trinomial, for x2 − 8x + ___?

8
16
–8
–16

Answer 1

Answer: 16

Step-by-step explanation: A more simple approach is realizing that the blocks show 8 x tiles and 1 x^2 tile. The 8 x tiles are on either side of the x^2 tile which is 4 x tiles on each side. So as we can see we can multiply each side together. 4x4 = 16. So that is how you get 16 without having to work it out.

Answer 2

`Perfect\ square:\ (x\pm y)^2=x^2\pm2xy+y^2\\therefore\\x^2-OK\\-8x=-2\cdot x\cdot 4\\4^2=16\\\\conclusion\\\\x^2-8x+\boxed{?}=x^2-2\cdot x\cdot4+\boxed{4^2}=x^2-8x+16\\\\Your\ answer:\boxed{\boxed{16}}`