Question

Which binomial is a difference of squares?
(Points : 1)
14x2 – 81

16x2 – 81

25x2 + 81

36x3 – 81

Answer 1

congrats on reaching ur 100th question :D

Answer 2

thank you!!

Answer 3

So a difference of squares we can write as \(\large a^2 - b^2\)

Lets look at the first option for an example

\[\large 14x^2 - 81\]

Now we need to make that look like \(\large a^2 - b^2\)

Well we know 81 = 9^2....but now what about 14? can that be written as something^2?

Answer 4

7

Answer 5

Hmm lets test that...7^2 = 49 ....so not quite :)

So since 14 cannot be written as a number^2 ....then this can NOT be a difference of squares

Answer 6

I hope that made sense? We basically want perfect squares to work with

1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25 etc...

Answer 7

So now lets move on to the third choice

\[\large 25x^2 + 81\]

Now notice...25 can be written as 5^2....so thats okay
and notice 81 can be written as 9^2

So we have

\[\large (5x)^2 \color\red{+} (9^2)\]

Now....this WOULD be perfect...except this is a SUM of squares...not a DIFFERENCE of squares

Answer 8

And now what about the second choice?

\[\large 16x^2 - 81\]

Since 16 can be written as 4^2....and 81 can be written as 9^2...we could write

\[\large (4x)^2 \color\red{-} (9)^2\]

And that is indeed a DIFFERENCE of squares (the minus sign) so our answer here would be B

Answer 9

ok thank you!

Answer 10

Did that at least make sense? Lol, but no problem :)

Answer 11

YES IT DID

Answer 12

Okay good :)