Question

Factorise the following:

xy⁷ – x⁷y

Answer 1

Given expression: xy⁷ – x⁷y

Step-wise calculation:

1. Notice that both terms have common factors of x and y. 

Take the common factors out:

xy⁷ – x⁷y = xy(y⁶) – xy(x⁶) 

xy⁷ – x⁷y = xy(y⁶ – x⁶)

2. Now factor the expression inside the parentheses (y⁶ – x⁶), which is a difference of squares and can be factored as:

y⁶ – x⁶ = (y³)² – (x³)²

y⁶ – x⁶ = (y³ – x³)(y³ + x³)

3. Further factor each cubic term using the difference and sum of cubes formulas:

y³ – x³ = (y – x)(y² + xy + x²) 

y³ + x³ = (y + x)(y² – xy + x²)