Question

factor the sum or differences of cubes.
1. X^3+1
2. 8x^3-125

Answer 1

Ok so the rule for sum or difference in cubes is:
\[a^3+b^3=(a+b)(a^2-ab+b^2)\]
and;\[a^3-b^3=(a-b)(a^2+ab+b^2)\]

Answer 2

So in your first problem what are the two cubes and are they sum or difference??

Answer 3

?

Answer 4

Ok so in your first problem a and b are x and 1 so plug that into the equation for sum of cubes.

Answer 5

Do you understand?

Answer 6

Look:
\[a^3+b^3=x^3+1^3\]

Answer 7

\[=(x+1)(x^2-(1)(x)+1^2)\]=\[(x+1)(x^2-x+1)\]

Answer 8

see how i plugged those into the equation for sum of cubes?

Answer 9

The way I remember the formula for sum and difference of cubes is using the mnemonic:
Same
Opposite
Always
Positive

This is referring to the addition or subtraction sign in a^3+b^3 or a^3-b^3:
As you can see in the factorization of the addition or sum of cubes the first "operation symbol" is the SAME as the addition symbol (+). The second one is the OPPOSITE of the addition symbol. and the third one is ALWAYS the addition symbol.

In the factorization of difference or subtraction of cubes . the first "operation symbol" is the SAME as the subtraction symbol (-). The second one is the OPPOSITE as subtractions ie. (+). and the third one is always POSITIVE ie. (+).

Answer 10

okay thank you so for the first one the answer would be (x+1)(x^2-x+1)

Answer 11

Now for your second problem it can be written as:\[(2x)^3+5^3\]so plug that into the difference of cubes formula:
\[(2x-5)((2x)^2+(5)(2x)+5^2)\]\[=(2x-5)(4x^2+10x+25)\]

Answer 12

Yah

Answer 13

Do you understand?

Answer 14

the SOAP thing kind of?

Answer 15

why is there a 2 and 5 only

Answer 16

the question is 8x^3-125

Answer 17

yes \[8x^3=(2x)^3\]

Answer 18

law of exponents:\[(ab)^3=a^3b^3\]

Answer 19

\[(2x)^3=2^3x^3\]

Answer 20

\[=8x^3\]

Answer 21

and btw 125 is 5^3

Answer 22

Just try to memorize the formulas for sum and difference of cubes it will really help you

Answer 23

i get i now thank you

Answer 24

glad to help