Evaluate (8a3−27b3)(64x3+y3), where (64x3+y3)≠0.
(2a−3b)(4a2+6ab+9b2)(4x+y)(16x2−4xy+y2)
Using the identity a3+b3=(a+b)(a2−ab+b2)
(64x3+y3)=(4x+y)(16x2−4xy+y2)
Using Identity a3−b3=(a−b)(a2+ab+b2)
(8a3−27b3)=(2a−3b)(4a2+6ab+9b2)
∴ (8a3−27b3)(64x3+y3)=(2a−3b)(4a2+6ab+9b2)(4x+y)(16x2−4xy+y2)