Question

Expand the following:

(5x − 4y)³

Answer 1

(5x − 4y)³

Using the identity:

(a − b)³ = a³ − 3a²b + 3ab² − b³

Here, a = 5x, b = 4y

(5x − 4y)³ = (5x)³ − 3(5x)²(4y) + 3(5x)(4y)² − (4y)³

= 125x³ − 3(25x²)(4y) + 3(5x)(16y²) − 64y³

= 125x³ − 3(100x²y) + 3(80xy²) − 64y³

∴ (5x − 4y)³ = 125x³ − 300x²y + 240xy² − 64y³