Answer:
True.
Step-by-step explanation:
It is because it is in the form [tex]a^2x^2+2abx+b^2[/tex] and this equals [tex](ax+b)^2[/tex].
Why it is in that form: well comparing [tex]a^2x^2+2abx+b^2[/tex], we have [tex]a=1, b=1[/tex]. Testing, plug in those values:
[tex](1)^2x^2+2(1)(1)x+(1)^2[/tex]
[tex]1x^2+2x+1[/tex]
[tex]x^2+2x+1[/tex].
This has the squared form of [tex](x+1)^2[/tex].
Test if you like:
[tex](x+1)^2[/tex]
[tex](x+1)(x+1)[/tex]
Use foil to expand:
First: x(x)=x^2
Outer: x(1)=x
Inner: 1(x)=x
Last: 1(1)=1
---------------Add together
[tex]x^2+2x+1[/tex]
It does indeed equal.
