Find the Product:
\[ (4x – 5y)(16x^2 + 20xy + 25y^2) \]
Solution:
Using identity:
\[ (a-b)(a^2+ab+b^2)=a^3-b^3 \]
Here, \[ a=4x,\qquad b=5y \]
\[ (4x – 5y)(16x^2 + 20xy + 25y^2) \]
\[ = (4x – 5y)\left[(4x)^2 + (4x)(5y) + (5y)^2\right] \]
\[ = (4x)^3 – (5y)^3 \]
\[ = 64x^3 – 125y^3 \]