Question

Which product will result in a sum or difference of cubes?

a) (x + 7)(x^2 – 7x + 14)
b) (x + 8)(x^2 + 8x + 64)
c) (x – 9)(x^2 + 9x + 81)
d) (x – 10)(x^2 – 10x + 100)

Answer 1

@UsukiDoll

Answer 2

sum of cubes formula
\[(a+b)(a^2-ab+b^2)\]
difference of cubes formula
\[(a-b)(a^2+ab+b^2)\]

Answer 3

c?

Answer 4

will give medal

Answer 5

I think the answer is C.

Answer 6

you think? mmmmm

Answer 7

Not really sure on this one. I was thinking either A. or C.

Answer 8

ah I see we have to go backwards on this..
so we need all perfect cubes. . no it can't be a.

Answer 9

Because it can't be factored right? @UsukiDoll

Answer 10

8 27 64

\[2^3 = 8 , 3^3 =27, 4^3 = 64, 5^3 = 125\]

Answer 11

@200205650 true and also 14 is not a perfect cube

Answer 12

okay

Answer 13

so its c?

Answer 14

sum of cubes
\[(a^3+b^3) = (a+b)(a^2-ab+b^2) \]

difference of cubes
\[(a^3-b^3) = (a-b)(a^2+ab+b^2) \]

Answer 15

these choices are wonky though

Answer 16

I don't see how you can factor any of them in the answer choices...unless you use the quadratic formula.

Answer 17

like .. let a = x
let b = 4
\[(a^3-b^3) = (a-b)(a^2+ab+b^2) \]
\[(x^3-4^3) = (x-4)(x^2+4x+16) \]

Answer 18

I see perfect squares for the last 3 choices that's true.. for the ending part is b^2 . It's like this question isn't following the rules. That's what's getting me mad

Answer 19

same here

Answer 20

let a = x and let b = 9
difference of cubes formula
\[(a^3-b^3) = (a-b)(a^2+ab+b^2) \]
\[(x^3-9^3) = (x-9)(x^2+9x+81) \]

Answer 21

From your examples so far @UsukiDoll I would think C. is the right answer.

Answer 22

that is messed up... really. 9 isn't a perfect cube to begin with. perfect square yes but not perfect cube

Answer 23

Ya it isn't...but the way the equations are set up B. and D. don't follow that same pattern.

Answer 24

only perfect cubes are allowed for these formulas...>:/
oh I'm missing something XD 9 x 9 x 9 = 729

Answer 25

729 is a perfect cube number. that guy is 9

Answer 26

ok I got it.. I missed a very important step
let a = x and b = 9
\[(x^3-729) = (x-9)(x^2+9x+81)\]
\[(x^3-9^3) = (x-9)(x^2+9x+81)\]

Answer 27

So the answer is C.?

Answer 28

that 729 is rewritten as 9^3 in the second line
so a = x (the variable) and b = 9 (the number)
a^2 = x^2
ab = 9x
b^2 = (9)(9) = 81

Answer 29

yeah C matches ... on top of that .. the signs match for the difference of cubes. I wasn't working backwards until the very beginning.

Answer 30

Great job explaining that!

Answer 31

well thank you guys for your time and patients :)

Answer 32

XD patience XDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD

Answer 33

It's past my lunch time too... so that's why my thinking started to go off