Question

1. $20c^{2}-45d^{2}$

Explanation:

Step1: Factor out the GCF

$20c^2 - 45d^2 = 5(4c^2 - 9d^2)$

Step2: Apply difference of squares

$4c^2 - 9d^2 = (2c)^2 - (3d)^2 = (2c-3d)(2c+3d)$

Step3: Combine factors

$5(2c-3d)(2c+3d)$

Answer:

$5(2c - 3d)(2c + 3d)$