Given:
[tex](y+4)^2-2(y+4)+1[/tex]
To find:
The factors.
Explanation:
i) Let us take,
[tex]t=y+4[/tex]
Substituting we get,
[tex]t^2-2t+1[/tex]
Factorizing we get
[tex]\begin{gathered} t^2-2t+1=t^2-t-t+1 \\ =t(t-1)-(t-1) \\ =(t-1)(t-1) \\ =(t-1)^2 \end{gathered}[/tex]
Replace the value of t in the above equation,
[tex]\begin{gathered} =(y+4-1)^2 \\ =(y+3)^2 \end{gathered}[/tex]
Therefore, the factored form of the polynomial is,
[tex](y+3)^2[/tex]
ii) Yes, this is the product of the perfect square trinomial.
So, Teresa is correct.
Final answer:
i) The factored form of the polynomial is,
[tex](y+3)^2[/tex]
ii) Teresa is correct.
