The perfect square trinomial in y = ( [tex]x^{2} + 2x + 1[/tex] ) -1 - 1 will be
⇒ [tex](x+1)^{2}[/tex]
The perfect square trinomial in y = (x + 2)2 - 1 - 1 will be
⇒ Null
A perfect square trinomial can be expressed as the square of a binomial,
We can write the first expression as,
y = [tex]x^{2} + 2x + 1[/tex]
y = [tex]x^{2} + 2x + 1 - 2[/tex]
⇒ [tex]x^{2} + x + x + 1[/tex]
⇒ [tex]x(x + 1) + 1(x + 1)[/tex]
⇒ (x + 1) (x + 1)
⇒ [tex](x + 1)^{2}[/tex]
Therefore, according to the first expression, [tex](x^{2} + 2x + 1) -1 - 1[/tex] is a perfect square binomial with the factor = [tex](x + 1)^{2}[/tex]
According to the second expression, y = (x +2)2 − 1 −1
This expression does not show any factors
Therefore, this second expression doesn't have any perfect square trinomial factors.
To learn more about perfect square trinomials,
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Factor the perfect-square trinomial in y = (x2 + 2x + 1) − 1− 1, y = (x +2)2 − 1 −1
