simplify (2√5+3√7)^2

Justify your answer

I posted this with no answer earlier. I hope i can get one now

Question

simplify (2√5+3√7)^2

Justify your answer

I posted this with no answer earlier. I hope i can get one now

tyteen4a03 · Answer

Remember that $(a + b)^2 = a^2 + 2ab + b^2$.

luigi0210 · Answer

It's the same as: 
$$(2\sqrt{5} +3\sqrt{7})*(2\sqrt{5} +3\sqrt{7})$$
Just multiply it out

anonymous · Answer

Okay, thanks

luigi0210 · Answer

It should be: 
$$4(5)+6(\sqrt{35})+6(\sqrt{35})+9(7)$$
Now just simplify

anonymous · Answer

20 + 36 + 36 + 63 = 155. Answer?

luigi0210 · Answer

Actually it be $$83+12\sqrt{35}$$

anonymous · Answer

oh.. so then whats the answer? Or is that the answer?

luigi0210 · Answer

That's the answer.

tyteen4a03 · Answer

@HatSimulator How did you get to 20 + 36 + 36 + 63?

Also, @Luigi0210 's step can be further simplified using my identity.

luigi0210 · Answer

Wait, you sure?

tyteen4a03 · Answer

@Luigi0210 Yes. Do you need proof?

anonymous · Answer

I'd like proof

tyteen4a03 · Answer

(a + b)^2
= (a + b)(a + b)
= a^2 + ab + ab + b^2
= a^2 + 2ab + b^2