a) x³ - 6x² + 12x - 8
= x³ - 3.x².2 + 3.x.2² - 2³
= (x - 2)³
b) 9x³ + 12x²y + 6xy² + y³
= x³ + (2x)³ + 12x²y + 6xy² + y³
= x³ + (2x + y)³
= (x + 2x + y)[x² - x(2x + y) + (2x + y)²]
= (3x + y)(x² - 2x² - xy + 4x² + 4xy + y²)
= (3x + y)(3x² + 3xy + y²)
\(a.x^3-6x^2+12x-8=x^3-3.x^2.2+3.x.2^2-2^3\)
\(=\left(x-2\right)^3.\)
\(b.9x^3+12x^2y+6xy^2+y^3\)
Câu b tính kiểu gì dộ.
a)
\(=\left(x^3-8\right)-\left(6x^2-12x\right)=\left(x-2\right)\left(x^2+2x+4\right)-6x\left(x-2\right)=\left(x-2\right)\left(x^2+2x+4-6x\right)=\left(x-2\right)\left(x^2-4x+4\right)=\left(x-2\right)\left(x-2\right)^2=\left(x-2\right)^3\)
b)
\(=\left(2x+y\right)^3-x^3=\left(2x+y-x\right)\left[\left(2x+y\right)^2+\left(2x+y\right)\cdot x+x^2\right]=\left(x+y\right)\left(4x^2+4xy+y^2+2x^2+xy+x^2\right)=\left(x+y\right)\left(7x^2+5xy+y^2\right)\)
