Question

Find the product of ( x- x^2) (x+x^2) (x^2+x^4)​

Answer 1

Answer:

$= (x^4 - x^8)$

Step-by-step explanation:

(Long Method, FOIL)

$(x-x^2)(x+x^2)(x^2+x^4)$

$=(x^2+x^3-x^3-x^4)(x^2+x^4)$

$= (x^2-x^4)(x^2+x^4)$

$= (x^4+x^6-x^6-x^8)$

$= (x^4 - x^8)$

(Short Method, Product of the Sum and Difference of a Binomial)

$(x-x^2)(x+x^2)(x^2+x^4)$

The product of the sum and difference of a binomial is the difference of the square of its first term and the square of its last term.

$=(x^2-x^4)(x^2+x^4)$

$= (x^4-x^8)$