Question

factorise:

9a (x − 2y)⁴ − 12a (x − 2y)³ 

Answer 1

9a (x − 2y)⁴ − 12a (x − 2y)³

The common factors between the terms are:

• a,
• (x − 2y)³, (the lower power of (x−2y),
• And the coefficients 9 and 12 have a common factor of 3.

Factor out 3a(x − 2y)³:

9a(x − 2y)⁴ − 12a(x − 2y)³ = 3a(x − 2y)³ (3(x − 2y) −4)

Simplify 3(x − 2y) −4:

3(x − 2y) −4 = 3x − 6y − 4

Thus, the expression becomes:

3a(x − 2y)³ (3x − 6y − 4)