I need to show that the right side equals the left side but I am having a little trouble simplifying.
k(2k+1) +(4(k+1)-1) = (k+1)(2(k+1)+1)
k^2+2k+3 For the right side?
LS = k(2k+1) +(4(k+1)-1)
= 2k^2 + k + 4k + 4 - 1
= 2k^2 + 5k + 3
RS = (k+1)(2(k+1)+1)
= (k+1)(2k+2+1)
= (k+1)(2k+3)
= 2k^2 + 5k + 3
mmmhh?
Thank you!
To show that the right side equals the left side, we need to simplify both sides of the equation and check if they are equal.
Let's start by simplifying the left side:
k(2k + 1) + (4(k + 1) - 1)
First, distribute k to the terms inside the parentheses:
= 2k^2 + k + (4(k + 1) - 1)
Next, simplify the expression inside the parentheses:
= 2k^2 + k + (4k + 4 - 1)
Combine like terms:
= 2k^2 + k + 4k + 3
Now, combine the remaining like terms:
= 2k^2 + 5k + 3
Now, let's simplify the right side of the equation:
(k + 1)(2(k + 1) + 1)
First, distribute (k + 1) to the terms inside the parentheses:
= (k + 1)(2k + 2 + 1)
Next, simplify the expression inside the parentheses:
= (k + 1)(2k + 3)
Now, distribute (k + 1) to the terms inside the parentheses:
= 2k^2 + 3k + 2k + 3
Combine like terms:
= 2k^2 + 5k + 3
Now, we can see that the right side simplifies to the same expression as the left side. Therefore, we have shown that both sides are equal:
Left side: 2k^2 + 5k + 3
Right side: 2k^2 + 5k + 3
Therefore, the right side does indeed equal the left side.