Gọi a+b =x có:  

a(x+b)³−b(x+a)³

 =a(x³+3x²b+3xb²+b³)−b(x³+3x²a+3xa²+a³)  

=ax³+3ax²b+3axb²+ab³−bx³−3bx²a−3bxa²−ba³  

=(a−b)x³+(3ax²b−3bx²a)+(3axb²−3bxa²)+ab³−ba³  

=(a−b)x³+3axb(b−a)+ab(b²−a²)  

=−x³(b−a)+3axb(b−a)+ab(b+a)(b−a)

 =−x³(b−a)+3axb(b−a)+(a²b+ab²)(b−a)

 =(b−a)(−x³+3axb+a²b+ab²)

nho lik e

a(a+2b)3 -b(2a+b)3

\(=a\left(a^3+6a^2b+12ab^2+8b^3\right)-b\left(8a^3+12a^2b+6ab^2+b^3\right)\)

\(=a^4+6a^3b+12a^2b^2+8ab^3-8a^3b-12a^2b^2-6ab^3-b^4\)

\(=a^4-2a^3b+2ab^3-b^4\)

\(=\left[\left(a^2\right)^2+ \left(b^2\right)^2\right]-2ab\left(a^2-b^2\right)\)

\(=\left(a^2+b^2\right)\left(a^2-b^2\right)-2ab\left(a^2-b^2\right)\)

\(=\left(a^2-b^2\right)\left(a^2-2ab+b^2\right)\)

\(=\left(a-b\right)\left(a+b\right)\left(a-b\right)^2\)

\(=\left(a-b\right)^3\left(a+b\right)\)

\(a.\left(a+2b\right)^3-b.\left(2a+b\right)^3\)

\(=a.\left(a+20+b\right)^3-b.\left(20+a+b\right)^3\)

\(=\left(a-b\right).\left(a+20+b\right)^3\)

Thế này có phải là phân tích đa thức thành nhân tử k ạ

Chúc bạn học tốt

\(a\left(a+2b\right)^3-b\left(2a+b\right)^3\)

\(=\left(a^4+6a^3b+12a^2b^2+8ab^3\right)-\left(b^4+8a^3b+12a^2b^2+6ab^3\right)\)

\(=a^4-b^4-2a^3b+2ab^3\)

\(=\left(a^2-b^2\right)\left(a^2+b^2\right)-2ab\left(a^2-b^2\right)\)

\(=\left(a^2-b^2\right)\left(a^2-2ab+b^2\right)\)

\(=\left(a-b\right)^3\left(a+b\right)\)

OK ?

a(a+2b)³-b(2a+b)³

=(2a+b)³.(a-b)

a( a+2b)^3 - b( 2a+b)^3

=a (a^3 + 2b^3) -b (2a^3 + b^3)

=a^4+ 2ab^3 - 2ab^3 - b^4

=( a^4-b^4) +(2ab^3-2ab^3)

=a-b

Chúc bạn hk tốt, k ch mk nha

`a^2 + ab + 2a + 2b = a(a+2) + b(a+2) = (a+b)(a+2)`