Please help me see the math involved in these function steps

Ih8Math

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Sep 7, 2014
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Let f be the function given by f(x) = x^2 + 2x − 3. Find the following function values: f(√3 + 1)

I get what they're asking me to do. They need me to substitute the latter for the X variable contained within the function.

So everywhere I see X, I replace with
√3 + 1



Here is the solution, step by step that i was provided with from the math book.
f(√3 + 1) = (√3 + 1)^2 + 2 · (√3 + 1) − 3

= (√3 + 1) · (√3 + 1) + 2 · (√3 + 1) − 3

=√3 ·√3+ 2 ·√3 + 1 · 1 + 2 ·√3 + 2 − 3

= 3 + 2 ·√3 + 1 + 2 ·√3 + 2 − 3
= 3 + 4 ·√3

I am not understanding AT ALL, what they are doing to arrive at the answer for the next time. This book is not actually doing out the math on paper so I have no idea how they're even coming up with some of these numbers. I'm a very visual learner when it comes to math and I won't get it unless all the work is done on paper.

Can anyone please explain the math they did to arrive at the next steps?
I cannot even begin to do this homework assigned unless I understand how to do it.
 
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