Question

Phân tích các đa thức sau thành nhân tử:

\(\frac{2}{5}x\left(y-1\right)-\frac{2}{5}y\left(y-1\right)\)

\(10x-25-x^2\)

\(\frac{1}{25}x^2-64y^2\)

\(x^3+\frac{1}{27}\)

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

\(8x^3+12x^2y+6xy+y^3\)

\(-x^3+9x^2-27x+27\)

Answer 1

\(\frac{2}{5}x\left(y-1\right)-\frac{2}{5}y\left(y-1\right)\)

\(=\left(y-1\right)\left[\left(\frac{2}{5}x-\frac{2}{5}y\right)\right]\)

\(=\left(y-1\right)\frac{2}{5}\left(x-y\right)\)

Answer 2

\(\frac{1}{25}x^2-64y^2\)

\(=\left(\frac{1}{5}x\right)^2-8^2\)

\(=\left(\frac{1}{5}x+8\right)\left(\frac{1}{5}x-8\right)\)

Answer 3

\(x^3+\frac{1}{27}=x^3+\left(\frac{1}{3}\right)^3\)

\(=\left(x+\frac{1}{3}\right)\left(x^2-\frac{1}{3}x+\frac{1}{9}\right)\)

\(8x^3+12x^2y+6xy+y^3\)

\(=2^3+3.4x^2y+3.2x.y^2+y^3\)

\(=\left(2+y\right)^3\)