I think you can make it a lot easier:
<md-toolbar>
<div class="md-toolbar-tools">
<span>Home</span>
<span flex></span>
<div>
<span>Sign Up</span>
<span>Sign In</span>
</div>
</div>
</md-toolbar>
You can insert a flexible element between the HOME and SIGNUP elements and it will fill the space between them.
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