factor as a trinomial square a^3-10a^2+25a

Question

it wants me to factor all of the problems as a trinomial square, and this is the only problem i can't figure out. please help me!

Answer 1

a^3-10a^2+25a

Take common out 'a' from given trinomial.

= a(a^2-10a+25)

Now factorize a^2-10a+25

= a^2-5a-5a+25

= a(a-5)-5(a-5)

= (a-5)(a-5)

= (a-5)^2

Factoring of a^3-10a^2+25a = a(a-5)^2