Toán phan tich da thuc thanh nhan tu: a^2b^2(a-b)+c^2b^2(b-c)+a^2c^2(c-a) 14/09/2021 By Adalynn phan tich da thuc thanh nhan tu: a^2b^2(a-b)+c^2b^2(b-c)+a^2c^2(c-a)
Ta có $a^2b^2(a-b)+c^2b^2(b-c)+a^2c^2(c-a) = b^2(a^3 – a^2b) + b^2(bc^2 – c^3) + a^2 c^2 (c-a)$ $= b^2(a^3 – c^3 + bc^2 – a^2b) + a^2 c^2 (c-a)$ $= b^2[(a-c)(a^2 + ac + c^2) + b(c^2 – a^2)] + a^2 c^2(c-a)$ $= b^2[(a-c)(a^2 + ac + c^2) -b(a-c)(a+c)] -a^2 c^2 (a-c)$ $= b^2(a-c)[a^2 + ac + c^2 – b(a+c)] – a^2 c^2(a-c)$ $= b^2(a-c)(a^2 + ac + c^2 – ba – bc -a^2 c^2)$ $= b^2(a-c)[a^2 – a^2c^2 + c(a+c) -b(a+c)]$ $= b^2(a-c)[a^2 – a^2c^2 + (a+c)(c-b)]$ Trả lời
Ta có
$a^2b^2(a-b)+c^2b^2(b-c)+a^2c^2(c-a) = b^2(a^3 – a^2b) + b^2(bc^2 – c^3) + a^2 c^2 (c-a)$
$= b^2(a^3 – c^3 + bc^2 – a^2b) + a^2 c^2 (c-a)$
$= b^2[(a-c)(a^2 + ac + c^2) + b(c^2 – a^2)] + a^2 c^2(c-a)$
$= b^2[(a-c)(a^2 + ac + c^2) -b(a-c)(a+c)] -a^2 c^2 (a-c)$
$= b^2(a-c)[a^2 + ac + c^2 – b(a+c)] – a^2 c^2(a-c)$
$= b^2(a-c)(a^2 + ac + c^2 – ba – bc -a^2 c^2)$
$= b^2(a-c)[a^2 – a^2c^2 + c(a+c) -b(a+c)]$
$= b^2(a-c)[a^2 – a^2c^2 + (a+c)(c-b)]$