Question

simplify(x3 ×y3) ÷{(x×y)2}2
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Answer 1

Step-by-step explanation:

x3 - y3

Simplify ———————

x2 - y2

Trying to factor as a Difference of Cubes:

1.1 Factoring: x3 - y3

Theory : A difference of two perfect cubes, a3 - b3 can be factored into

(a-b) • (a2 +ab +b2)

Proof : (a-b)•(a2+ab+b2) =

a3+a2b+ab2-ba2-b2a-b3 =

a3+(a2b-ba2)+(ab2-b2a)-b3 =

a3+0+0-b3 =

a3-b3

Check : x3 is the cube of x1

Check : y3 is the cube of y1

Factorization is :

(x - y) • (x2 + xy + y2)