I cant really seem to factor (x^3+a^3).. can someone help me step by step......?

Question

I cant really seem to factor (x^3+a^3).. can someone help me step by step......?

Answer 1

f(x) = x^3 + a^3

by inspection f(-a) = 0

so x + a is a factor

by division x^3+a^3 = (x+a)(x^2- ax + a^2)

math kp

Answer 2

This is the sum of two cubes, which can be remembered

x^3 + a^3 = (x + a)(x^2 - ax + a^2)

You might guess that (x + a) is a factor, and try the division

. . . . . x^2 - ax + a^2

. . . . . - - - - - - - - - - - - - - - - - - - -

x + a ) x^3 + 0ax^2 + 0a^2x + a^3

. . . . . x^3 + 1ax^2

. . . . . - - - - - - - - -

. . . . . . . . - 1ax^2 + 0a^2x

. . . . . . . . -1ax^2 - 1a^2x

. . . . . . . . .- - - - - - - - - - -

. . . . . . . . . . . . . . + 1a^2x + a^3

. . . . . . . . . . . . . . + 1a^2x + a^3

. . . . . . . . . . . . . . - - - - - - - - - - -

Answer 3

(x^3+a^3)=(x+a)(x^2-ax+a^2)

Answer 4

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

x^3 + a^3 = (x + a)(x^2 - xa + a^2)

Answer 5

(x^3+a^3)

=(x+a)(x^2-ax+9)

Answer 6

hi there...

the answer is : (x+a)(x^2 - ax + a^2), but how?

here....

if you make a substitution of x = -a into the term, you will get the result is 0 (factor theorem).

(-a)^3 + a^3 = -a^3 +a^3= 0 see...?

then ( x + a) is one of the factor of (x^3+a^3).

to get the other factors, just do long division...

( x^3 + a^3) / (x+a), then in the quotient part  u will get (x^2- ax + a^2), so the factors of (x^3+a^3)=(x+a)(x^2 - ax + a^2)