How do you factor an expression a cubed exponent?

Question

like x^3+8? and can you explain how you got it? Is there a specific way for factoring expressions with a cubed exponet?

Answer 1

a³ + b³ = (a+b)(a²-ab+b²)

a³ + 8
= a³ + 2³
= (a+2)(a²-2a+2²)
= (a+2)(a²-2a+4)

Similarly:
a³-b³ = (a-b)(a²+ab+b²)

Answer 2

It is not as easy to do as quadratics, the way i do it is to guess a form of the solution:

x³ + 8 = (x + A)(x² + Bx + C)
expand the right
x³ + 8 = x³ + Bx² + Cx + Ax² + ABx + AC

group the like terms
x³ + 8 = x³ + x²(B + A) + x(C + AB) + AC

you know that since there is no x² term B + A = 0, for the same reason C + AB = 0 and then AC = 8

You can solve and you should get

(x+2)(x² - 2x + 4)

you can also use synthetic division but i dislike that.

Answer 3

cube root(16x^15y^7z^11) first ruin the selection (sixteen) into 2 products the place one among them is a cube root: sixteen = 8 * 2 the place 8 is a cube root that's 2. so as that comes out 2cuberoot(2x^15y^7z^11) now take each and each exponent and divide it via the cost of the basis (on condition that we are cube rooting, which skill the cost of the basis is 3) 15/3 = 5 r0 7/3 = 2 r1 11/3 = 3 r2 the quotient tells you tactics lots of that variable comes out and something tells you tactics many stay in: 2x^5y^2z^3*cuberoot(2yz^2) voila

Answer 4

If it has the root x=-2,by synthetic division you get
x^3+8=(x+2)(x^2-2x+4)

Answer 5

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