Difference of squares? (Also LaTex)

Can someone explain step two of this problem a little bit more in depth to me?

From what I can tell if using the difference of squares

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

10^25 + 25 = a 10^25 - 25 = b

So how exactly does (a - b) = (10^25 + 25 - 10^25 + 25) in step two?

Shouldn't it be (10^25 + 25 - 10^25 - 25)? How does the minus sign in b become a plus?

Also, how do you write Latex on this site? I'm new here and can't seem to get it to work.

/[ 2^{34} /] <- Is this not right?

Easy Math Editor

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Comments

Negative signs are distributive across parentheses i.e. $-(x + y) = -x - y.$ Think of it as multiplying each term by -1. We can write $10^{25} - 25$ as $10^{25} + (-25),$ so that

$-b = -(10^{25} + (-25)) = -10^{25} - (-25) = -10^{25} + 25,$

and $a - b = a + (-b) = 10^{25} + 25 - 10^{25} + 25,$ as desired.

Also, welcome to Brilliant! On this site, $\LaTeX$ is enclosed with $\backslash ( \, \cdots \backslash )$ for in-line text or with $\backslash [ \, \cdots \backslash ]$ for paragraphical text. I hope this answers your questions!

Steven Yuan - 3 years, 2 months ago

Man, how did I miss something as simple as the distributive property? I have got a long way to go, huh.

Also, I just realized that latex use backslash, not forwards slash. Oh well, gotta make mistakes before you solve them I guess.

Thanks!

Steven Stavrakis - 3 years, 2 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$