Question

positive
a^3+b^3=(a+b)(a^2-ab+b^2)

negative
a^3-b^3=(a-b)(a^2+ab+b^2)

4.) x^3+1000=0 (factor the cubic)

(5 and 6 factor the polynomial)


5.) 8x^3+64=0


6.)216x^3+27=0

Answer 1

@adrianluvvsyouu2

Answer 2

Whats the question?

Answer 3

4-6

Answer 4

theyre numbered its factoring polynomials

Answer 5

The fourth one is basically the formula I used earlier

a^3 - b^3 = (a-b)(a^2 - ab + b^2)
a^3 + b^3 = (a+b)(a^2 - ab + b^2) <-- Try using this one

Basically you need to change 1000 into a number to the third power, said number is b, and x is a.

Answer 6

Same thing with the other two, change the values into a number to the third power (cubed)

So 8 is the same as 2^3.. 64 is the same as 4^3.. this way you can plug them into this formula every single time without fail

Answer 7

im confused

Answer 8

how do i write it

Answer 9

You want it in either of these forms

(a+b)(a^2 - ab + b^2) or (a-b)(a^2 - ab + b^2), depending on original expression.. if the two terms have a plus in between them, you use the formula that has (a+b), if the two terms have a minus between them you use the formula that has (a-b)

Let me use an example with the first problem.. We have x^3 + 1000

The first thing I want to do is get it into the form a^3 + b^3, so that the formula works

Basically, I already have x^3, now I just need to change 1000 into a number to the third power. 1000 is the same as 10^3, so I want to rewrite this as

x^3 + 10^3, now it's in the same form as a^3 + b^3
where x = a
and 10 = b

Then I can plug this into the larger formula (a+b)(a^2 - ab + b^2)
notice how I used the formula with the (a+b)? This is because the original expression had a plus between the two terms

So now I can say, for every a in that formula, I just need to put an x
For every b in that formula, I just need to put a 10...

(x + 10)(x^2 - x * 10 + 10^2)
Simplified to (x+10)(x^2 - 10x + 100)

Answer 10

thank you can u help me with the other 2

Answer 11

its not even a quiz its ok. ill find someone else.

Answer 12

Hey! I'm learning this in Algebra 2 right now, I can definitely help you. :3

Answer 13

thank youuuu

Answer 14

I can help you with 5 and 6 first, I'm much more familiar with these.

Answer 15

#5: Your equation is \[8x^3+64=0\], and you must use the formula to find the sum of cubes (since you are adding.) and the formula is: \[a^3 + b^3 = (a+b)(a^2 − ab + b^2 )\]

Answer 16

So first we take out the GCF (Greatest Common Factor), what's the biggest number that can go into both 8 and 64? (You tell me. :p)