Question

(2a+3b)cube - (2a-3b)cube. factories it

Answer 1

We know that,
$(a+b)^3 - (a-b)^3 = 6a^2b + 2b^3$

$(2a+3b)^3 - (2a-3b)^3 = 6(2a)^2(3b) + 2(3b)^3$

$(2a+3b)^3 - (2a-3b)^3 = 6*4a^2*3b + 2*27b^3$

$(2a+3b)^3 - (2a-3b)^3 = 72a^2b + 54b^3$

$(2a+3b)^3 - (2a-3b)^3 = (18b)(4a^2 + 3b^2)$

Answer 2

Factorization.  we know that   
x³ - y³ = (x - y) (x²+xy+y²)            in our problem: x = 2a+3b    y =2a-3b
Substituting we staightway get two factors. We donot have to remember complicated formula.

  = [ 2a+3b-(2a-3b) ] [ (2a+3b)²+(2a+3b)(2a-3b)+(2a-3b)² ]
  = [ 6 b ] [(4a² + 9b² + 12ab) +(4a² - 9b²) + (4a²+9b²-12ab) ]
  = 6 b [ 12 a² +9b² ]    = 18 b [ 4a² + 3 b² ]