what is the polynomial 3y² + (y + 7)² - 15 after it has been fully simplified and written in standard…

what is the polynomial 3y² + (y + 7)² - 15 after it has been fully simplified and written in standard form?\n4y² + 34\n3y² + y + 34\n4y² + 14y + 34\n4y⁴ + 34

what is the polynomial 3y² + (y + 7)² - 15 after it has been fully simplified and written in standard form?\n4y² + 34\n3y² + y + 34\n4y² + 14y + 34\n4y⁴ + 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 get $(y + 7)^2=y^{2}+14y + 49$.

Step2: Substitute and combine like - terms

The original polynomial is $3y^{2}+(y + 7)^2-15$. Substitute $(y + 7)^2=y^{2}+14y + 49$ into it: $3y^{2}+y^{2}+14y + 49-15=(3y^{2}+y^{2})+14y+(49 - 15)$. Combining like - terms: $4y^{2}+14y + 34$.

Answer:

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