Question

Prove that the value of the expression: (125^2+25^2)(5^2-1) is divisible by 39

Answer should be written ___*39

Answer 1

10000*39

Explanation:

Simplify the equation fully.

(125 + 25)(5 - 1)

(15625 + 625)(25 - 1)

(16250)(24)

390000

Divide the answer by 39

390000/39 = 10000

Answer 2

10000 * 39

Explanation:

(125^2+25^2)(5^2-1)

Rewriting

(5^3^2+5^2^2)(5^2-1)

We know that a^b^c = a^ ( b*c)

(5^(3*2)+5^(2*2))(5^2-1)

(5^6+5^4)(5^2-1)

Factor out 5^4

5^4( 5^2 +1)(5^2-1)

5^4 ( 26) (24)

Factor

5^4 ( 13*2) (3*8)

Rearrange the order

5^4 ( 13*3) (2*8)

5^4 *39 *16

625 * 16 * 39

10000 * 39