Question

X^2+2x+1 is a perfect square trinomial

True of False?

Answer 1

True.

Explanation:

It is because it is in the form
`a^2x^2+2abx+b^2` and this equals
`(ax+b)^2`.

Why it is in that form: well comparing
`a^2x^2+2abx+b^2`, we have
`a=1, b=1`. Testing, plug in those values:

`(1)^2x^2+2(1)(1)x+(1)^2`

`1x^2+2x+1`

`x^2+2x+1`.

This has the squared form of
`(x+1)^2`.

Test if you like:

`(x+1)^2`

`(x+1)(x+1)`

Use foil to expand:

First: x(x)=x^2

Outer: x(1)=x

Inner: 1(x)=x

Last: 1(1)=1

---------------Add together

`x^2+2x+1`

It does indeed equal.