a: \(x^2+2x-8\)
\(=x^2+2x+1-9\)
\(=\left(x+1\right)^2-9=\left(x+1-3\right)\left(x+1+3\right)\)
=(x-2)(x+4)
b: \(x^2+5x+6\)
\(=x^2+5x+\frac{25}{4}-\frac14\)
\(=\left(x+\frac52\right)^2-\left(\frac12\right)^2=\left(x+\frac52-\frac12\right)\left(x+\frac52+\frac12\right)\)
=(x+2)(x+3)
c: \(4x^2-12x+8\)
\(=4x^2-12x+9-1\)
\(=\left(2x-3\right)^2-1\)
=(2x-3-1)(2x-3+1)
=(2x-4)(2x-2)
=4(x-2)(x-1)
d:Sửa đề: \(x^2-xy-\frac34y^2\)
\(=x^2-xy+\frac14y^2-y^2\)
\(=\left(x-\frac12y\right)^2-y^2\)
\(=\left(x-\frac12y-y\right)\left(x-\frac12y+y\right)=\left(x-\frac32y\right)\left(x+\frac12y\right)\)
e: \(x^2+10x+16\)
\(=x^2+10x+25-9\)
\(=\left(x+5\right)^2-9=\left(x+5+3\right)\left(x+5-3\right)\)
=(x+8)(x+2)
f: \(9x^2-24x+15\)
\(=9x^2-2\cdot3x\cdot4+16-1\)
\(=\left(3x-4\right)^2-1=\left(3x-4-1\right)\left(3x-4+1\right)\)
=(3x-5)(3x-3)
=3(x-1)(3x-5) \(\)
