factorize a^2(b-c)^3+5^2(c-a)^3+c^2(a-b)
Answers
Step-by-step explanation:
The given expression, is homogeneous and cyclic in a, b and c, and is of degree 5.
p = (a - b)(b - c)(c - a) is cyclic of degree 3.
If E = p.q, then q should be homogeneous and cyclic in a, b and c, and is of degree 2.
The most general expression of q is then m(a2+b2+c2)+n(ab+bc+ca)m(a2+b2+c2)+n(ab+bc+ca); for some m and n.
Thus, E=(a−b)(b−c)(c−a)[m(a2+b2+c2)+n(ab+bc+ca)]E=(a−b)(b−c)(c−a)[m(a2+b2+c2)+n(ab+bc+ca)]
m and n can be obtained by comparing coefficients. [Subsequently, found the following is simpler. See also problem # 465127.]
m and n can also be obtained by substituting 2 different sets of values for a, b, and c.
PLEASE MARK ME AS BRAINLIEST AND FOLLOW ME AND THANK ME AND DON'T FORGET TO GIVE ME MORE POINTS.....PLEASE