Answer:
194
Step-by-step explanation:
Recall 2 rules to solve this easily:
1. [tex](a+b)^2=a^2+2ab+b^2[/tex]
2. [tex](a-b)^2=a^2-2ab+b^2[/tex]
Now, if we let a = 7 and [tex]b=4\sqrt{3}[/tex], we can say the problem is basically of the form:
[tex](a+b)^2 + (a-b)^2[/tex]
This can be simplified using the rules:
[tex](a+b)^2 + (a-b)^2\\a^2+2ab+b^2+a^2-2ab+b^2\\2a^2+2b^2[/tex]
Now we can plug the values of a and b we initially thought of (remember though [tex]\sqrt{x} \sqrt{x} =x[/tex]):
[tex]2a^2+2b^2\\2(7)^2+2(4\sqrt{3})^2\\ 2(49)+2(4\sqrt{3})(4\sqrt{3})\\98+2(4)(4)(\sqrt{3} )(\sqrt{3} )\\98+2(4)(4)(3)\\98+96 \\194[/tex]
194 is the final answer.
