Question

(3x+5y)³+3(3x+5y)²(2x-5y)+3(3x+5y)(2x-5y)²+(2x-5y)³​

Answer 1

Answer:

Let 3x + 5y  =  a and 2x - 5y  =  b

therefore now the problem would be

a^3 + 3a^2b + 3ab^2 + b^3  (since ( a+ b)^3  = a^3 + 3a^2b + 3ab^2 + b^3  )

therefore after factorizing we will get (a + b)^3

after resubstituting a = 3x + 5y and b = 2x - 5y

we will get (3x + 5y + 2x - 5y)^3

add the like terms - (5x)^3

therefore the answer is 125x^3

Step-by-step explanation:

Answer 2

(2x -5y)3 – (2x + 5y)3 = [(2x)3 – (5y)3 – 3(2x)(5y)(2x – 5y)]

-[(2x)3 + (5y)3 + 3(2x)(5y)(2x+5y)]

[using identity, (a – b)3 = a3 -b3 – 3ab and (a + b)3 =a3 +b3 + 3ab] = (2x)3 – (5y)3 – 30xy(2x – 5y) – (2x)3– (5y)3 – 30xy (2x + 5y)

= -2 (5y)3 – 30xy(2x – 5y + 2x + 5y)

= -2 x 125y3 – 30xy(4x) = -250y3 -120x2y