Could somebody show me how to simplify this?(5√2-1)²

Question

mayankdevnani · Answer

welcome to openstudy!

anonymous · Answer

Thanks! :)

mayankdevnani · Answer

did you try it ?

anonymous · Answer

Yeah, I tried to simplify it myself, but I'm not entirely sure where to start.

anonymous · Answer

Do I get the √2 first before I try and solve it?

mayankdevnani · Answer

use
$$\large \bf (a-b)^2=a^2+b^2-2ab$$

anonymous · Answer

Ahh, so I'm missing a formula, makes sense, lol. Thanks! I can take it from here.

mayankdevnani · Answer

good !

anonymous · Answer

Well, I thought I could figure it out with the formula... Sorry, I have not a single clue what to do with that formula. There is no a or b in (5√2-1)² could you show me how to apply the formula to the question please?

mayankdevnani · Answer

$$\large \bf (5 \sqrt2)^2+(1)^2-2(5\sqrt{2})(1)$$

phi · Answer

you don't need a formula, but it helps to memorize them if you want to be "fast"

the little 2 in the upper right means "square"  or multiply by itself
$$ ( 5 \sqrt{2} -1 ) ( 5 \sqrt{2} -1 ) $$
have you learned FOIL to multiply "binomials"?

phi · Answer

the F in FOIL means "first"  which is to remind you to multiply the two "first" terms:
$$ 5 \cdot \sqrt{2} \cdot  5 \cdot \sqrt{2}  \= 5 \cdot 5 \cdot  \sqrt{2} \cdot   \sqrt{2} $$