Question

Medal
Simplify

(1/6)^2 - (-1/6)^2

Answer 1

ok well lets put this equation together ok @harz360

Answer 2

ok

Answer 3

\[\frac{ 1 }{ 6 }\div2-\frac{ -1 }{ -6 }\] Correct?

Answer 4

wait did that wrong srry

Answer 5

its ok

Answer 6

\[\left( \frac{ 1 }{ 6 } \right)\div2-\left( \frac{ -1 }{ -6 } \right)\div2\]

Answer 7

there is that right?

Answer 8

Where did you get the 2 from

Answer 9

isnt the equation have ^2? that mean divided right?

Answer 10

2 is the exponent

Answer 11

oh lol srry

Answer 12

@TheSmartOne

Answer 13

im not too good at exponents sorry ill try to get some help :)

Answer 14

@dan815 @perl @BloomLocke367

Answer 15

Let's look at the quantity
\[(-\frac{1}{6})^2 = (-1 *\frac{1}{6})^2\]

What is -1 squared?

Answer 16

there you go lol ur way better than me lol

Answer 17

ok how would you solve that

Answer 18

What's -1 * -1?

Answer 19

1

Answer 20

Use the formula a^2 - b^2 = (a-b)(a+b) ...

Answer 21

Excellent. Using this, we can say
\[(-\frac{1}{6})^2 = (\frac{1}{6})^2\]
Can you see what it simplifies to now?

Answer 22

yes

Answer 23

so we dont use the exponent?

Answer 24

There are a few approaches. Shiraz gave one that is 100% valid. My approach "used" the exponent to show that we can "drop" the negative sign, since when we square a negative quantity, it's result is positive.

We're then left with
\[(\frac{1}{6})^2 - (\frac{1}{6})^2\]
Which we can easily see goes to...

Answer 25

yes now what is the next step

Answer 26

We can solve it from there. We have a number (1\6)^2. We're then subtracting the same number from it.

x-x = ?

Answer 27

x-x = 0

Answer 28

Yep.

So
\[(\frac{1}{6})^2 - (\frac{1}{6})^2 = ?\]

Answer 29

Squaring a number is the same as multiplying the number by itself like 6*6
so that would be 36
(1/36)-(1/6)^2
Squaring the expression is the same as multiplying the expression by itself twice
1/36((-1/6)(-1/6))
1/36-1/36
Combine the numerators of all fractions
1/36(1-1) so subtract 1-1 and you get 0
0/36
what is an expression with zero in the numerator?

Answer 30

0

Answer 31

There you go :)

Answer 32

but dont the 2 minus signs become positive signs?

Answer 33

That's right 0

Answer 34

The second "minus" sign is inside the squared term.

We know that
\[(a*b)^2 = a^2 * b^2\]
so
\[(-\frac{1}{6})^2 = (-1)^2*(\frac{1}{6})^2 = (\frac{1}{6})^2\]

Answer 35

ohh i c so the answer is just 0?

Answer 36

Yup :)

Answer 37

thank you both i am confused on who to give the medal to lol