y+y^2+(y+y)^2= ?
a. y^2 + 5y
b. 2y^2 + y
c. 3y^2 + y
d. 5y^2 + y
e. 4y^4 + y^2 + y
please answer and explain
y+y^2+(y+y)^2
= y + y^2 + (2y)^2
= y + y^2 + 4y^2
= y + 5y^2
d)
thank you, Reiny
To simplify the given expression y+y^2+(y+y)^2, we can follow these steps:
Step 1: Simplify the terms inside parentheses
In the expression (y+y), we can combine the two y terms to get 2y.
Step 2: Evaluate the square term
(y+y)^2 can be expanded using the formula (a+b)^2 = a^2 + 2ab + b^2.
In this case, a = y and b = y, so substituting in the formula we get:
(y+y)^2 = y^2 + 2(y)(y) + y^2
Simplifying further, we have:
(y+y)^2 = y^2 + 2y^2 + y^2 = 4y^2
Step 3: Combine like terms
Now, we can combine the y term with the y^2 term to get:
y + y^2 + (y+y)^2 = y^2 + y + 4y^2
Step 4: Simplify the expression
Combine the two y^2 terms and the y term:
y^2 + y + 4y^2 = 5y^2 + y
Therefore, the simplified form of the given expression is 5y^2 + y. So, the correct answer is option d.