So the semester just started and im already drowning. Im usually pretty good at math but I just dont get proofs.

I need help with a few problems (ive already attempted them multiple times), ill just post one at a time.

The first one:

from 'Mathematical Thinking Problem Solving and Proofs 2nd ed.'

1.29

Let x,y,z be nonnegative real numbers such that y+z > or = to 2.

Prove: (x+y+z)^2 is > or = 4x + 4yz

My attempt

I expanded the square and canceled out what I could.

Than I attempted different things from moving the right side over to the left and seeing if I could simply, or grouping the left and seeing if they broke down into smaller elements..

This is not graded homework just practice but the quizzes are very similar to the HW im told so I need to understand this.

Thanks in advance!