Question

Factorize #) 27x^3- 30x^2y + 40xy^2 - 64y^3

Answer 1

Step-by-step explanation:

Given :-

27x³ - 30x²y + 40xy² - 64y³

To find :-

Factorize the given expression ?

Solution :-

Given expression is 27x³-30x²y+40xy²-64y³

It can be written as

=> (27x³-64y³)-(30x²y-40xy²)

=> [(3x)³-(4y)³]-10xy(3x-4y)

=> (3x-4y)[(3x)²+(3x)(4y)+(4y)²]-10xy(3x-4y)

Since,a³-b³ = (a-b)(a²+ab+b²)

=> (3x-4y)(9x²+12xy+16y²)-10xy(3x-4y)

=> (3x-4y)(9x²+12xy+16y²-10xy)

=> (3x-4y)(9x²+2xy+16y²)

Therefore,27x³-30x²y+40xy²-64y³ is

(3x-4y)(9x²+2xy+16y²)

Answer:-

Factorization of 27x³ - 30x²y + 40xy² - 64y³ is

(3x-4y)(9x²+2xy+16y²)

Used formulae:-

→ a³-b³ = (a-b)(a²+ab+b²)