Phân tích đa thức thành nhân tử
a) Ta có: \(7x^2-42x+63\)
\(=7\left(x^2-6x+9\right)\)
\(=7\left(x-3\right)^2\)
b) Ta có: \(5x^3-15x^2+10xy\)
\(=5x\left(x^2-3x+2y\right)\)
c) Ta có: \(12ax+16y^2-4a^2-9x^2\)
\(=-\left(4a^2-12ax+9x^2-16y^2\right)\)
\(=-\left\{\left[\left(2a\right)^2-2\cdot2a\cdot3x+\left(3x\right)^2\right]-\left(4y\right)^2\right\}\)
\(=-\left[\left(2a-3x\right)^2-\left(4y\right)^2\right]\)
\(=-\left(2a-3x-4y\right)\left(2a-3x+4y\right)\)
d) Ta có: \(2a^3b+4a^2b^2+6ab^3\)
\(=2ab\left(a^2+2ab+3b^2\right)\)
e) Ta có: \(4x^3-7x^2-2x\)
\(=x\left(4x^2-7x-2\right)\)
\(=x\left(4x^2-8x+x-2\right)\)
\(=x\left[4x\left(x-2\right)+\left(x-2\right)\right]\)
\(=x\left(x-2\right)\left(4x+1\right)\)