a: \(18x^3-\dfrac{8}{25}x=2x\left(9x^2-\dfrac{4}{25}\right)=2x\left(3x-\dfrac{2}{5}\right)\left(3x+\dfrac{2}{5}\right)\)
b: \(a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
\(=a\left(a^3+6a^2b+12ab^2+8b^3\right)-b\left(8a^3+12a^2b+6ab^2+b^3\right)\)
\(=a^4+6a^3b+12a^2b^2+8ab^3-8a^3b-12a^2b^2-6ab^3-b^4\)
\(=\left(a^4-b^4\right)+\left(6a^3b-6ab^3\right)+\left(8ab^3-8a^3b\right)\)
\(=\left(a-b\right)\left(a+b\right)\left(a^2+b^2\right)+6ab\left(a^2-b^2\right)+8ab\left(b^2-a^2\right)\)
\(=\left(a-b\right)\left(a+b\right)\left(a^2+b^2+6ab-8ab\right)\)
\(=\left(a-b\right)^3\cdot\left(a+b\right)\)
a) \(18x^3-\dfrac{8}{25}x\)
\(=\dfrac{2}{25}x\left(225x^2-4\right)\)
\(=\dfrac{2}{25}x\left(15x-2\right)\left(15x+2\right)\)
b) \(a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
\(=a^4+6a^3b+12a^2b^2+8ab^3-8a^3b-12b^2a^2-6ab^3-b^4\)
\(=a^4-2a^3b+2ab^3-b^4\)
\(=a^4-3a^3b+3a^2b^2-ab^3+a^3b-3a^2b^2+3ab^3-b^4\)
\(=a\left(a^3-3a^2b+3ab^2-b^3\right)+b\left(a^3-3a^2b+3ab^2-b^3\right)\)
\(=\left(a+b\right)\left(a^3-3a^2b+3ab^2-b^3\right)\)
\(=\left(a+b\right)\left(a-b\right)^3\)
Câu c đã được phân tích r nha
