Question

Phân tích thành nhân tử :

a) \(\left(x+y\right)^2-\left(x-y\right)^2\)

b) \(\left(3x+1\right)^2-\left(x+1\right)^2\)

c) \(x^3+y^3+z^3-3xyz\)

Answer 1

a) \(\left(x+y\right)^2-\left(x-y\right)^2\)

\(\Leftrightarrow\left[\left(x+y\right)+\left(x-y\right)\right]\left[\left(x+y\right)-\left(x-y\right)\right]\)

\(\Leftrightarrow\left(x+y+x-y\right)\left(x+y-x+y\right)\)

\(\Leftrightarrow2x.2y=4xy\)

b) \(\left(3x+1\right)^2-\left(x+1\right)^2\)

\(\Leftrightarrow\left[\left(3x+1\right)+\left(x+1\right)\right]\left[\left(3x+1\right)-\left(x+1\right)\right]\)

\(\Leftrightarrow\left(3x+1+x+1\right)\left(3x+1-x-1\right)\)

\(\Leftrightarrow\left(4x+2\right).2x\)

\(\Leftrightarrow8x^2+4x\)

\(\Leftrightarrow x\left(8x+4\right)\)