What is the answer (5x+2)^4, using binomial theorem?

Question

I would like to get the anwer because I am not getting it.

Answer 1

(5x + 2)^4

From the binomial therom

(x +y )^4 = x ^4 + 4x ^3y + 6x ^2y ^2 + 4xy ^3 + y ^4

Now we write out the expansion of (5x + 2)^4

x  = 5x  and y  = 2.

(5x + 2)^4 = (5x )^4 + 4(5x )^3 (2) + 6(5x )^2(2)^2 + 4(5x )(2)^3+ (2)^4

= 625x ^4 + 4(125x ^3)2 + 6(25x ^2)(4) + 4(5x )(8) + 16

= 625x ^4 + 1000x ^3 + 600x ^2 + 160x + 16

(5x + 2)^4 = 625x ^4 + 1000x ^3 + 600x ^2 + 160x + 16.