what is the polynomial $3y^{2}+(y + 7)^{2}-15$ after it has been fully simplified and written in standard…

what is the polynomial $3y^{2}+(y + 7)^{2}-15$ after it has been fully simplified and written in standard form?\n$4y^{2}+34$\n$3y^{2}+y + 34$\n$4y^{2}+14y + 34$\n$4y^{4}+34$

what is the polynomial $3y^{2}+(y + 7)^{2}-15$ after it has been fully simplified and written in standard form?\n$4y^{2}+34$\n$3y^{2}+y + 34$\n$4y^{2}+14y + 34$\n$4y^{4}+34$

Answer

Explanation:

Step1: Expand $(y + 7)^2$

Using the formula $(a + b)^2=a^{2}+2ab + b^{2}$, where $a = y$ and $b = 7$, we have $(y + 7)^2=y^{2}+14y + 49$. So the original polynomial $3y^{2}+(y + 7)^{2}-15$ becomes $3y^{2}+y^{2}+14y + 49-15$.

Step2: Combine like - terms

Combine the $y^{2}$ terms: $3y^{2}+y^{2}=4y^{2}$. Combine the constant terms: $49-15 = 34$. The polynomial simplifies to $4y^{2}+14y + 34$.

Answer:

$4y^{2}+14y + 34$