a) 2x2 + 4x + xy + 2y
= (2x2 + xy) + (4x + 2y)
= x(2x + y) + 2(2x + y)
= (x + 2)(2x + y)
b) x2 + xy - 7x - 7y
= x(x + y) - 7(x + y)
= (x - y)(x + y)
c) x2 + 2xy + y2 - 4
= (x + y)2 - 22
= (x + y - 2)(x + y + 2)
d) 1 - y3 + 6xy2 - 12x2y + 8x3
= 1 - [y3 - 3 . 2x . y2 + 3 . (2x)2 . y + (2x)3]
= 13 - (y - 2x)3
= (1 - y + 2x)[1 - y + 2x + (y - 2x)2]
b) x2 + xy - 7x - 7y
= x(x + y) - 7(x + y)
= (x + y)(x-7)
\(a,2x^2+4x+xy+2y\)
\(=\left(2x^2+xy\right)+\left(4x+2y\right)\)
\(=x\left(2x+y\right)+2\left(2x+y\right)\)
\(=\left(x+2\right)\left(2x+y\right)\)
\(b,x^2+xy-7x-7y\)
\(=\left(x^2+xy\right)+\left(-7x-7y\right)\)
\(=x\left(x+y\right)-7\left(x+y\right)\)
\(=\left(x-7\right)\left(x+y\right)\)
\(c,x^2+2xy+y^2-4\)
\(=\left(x+y\right)^2-2^2\)
\(=\left(x+y-2\right)\left(x+y+2\right)\)
\(d,1-y^3+6xy^2-12x^2y+8x^3\)
\(=1-\left(y^3-6xy^2+12x^2y-8x^3\right)\)
\(=1-\left(y-2x\right)^3\)
\(=1^3-\left(y-2x\right)^3\)
\(=\left(1-y+2x\right)\left(1+y-2x+y^2-4x^2\right)\)
\(e,b^2c+bc^2+ac^2-a^2c-ab\left(a+b\right)\)
\(=\left(b^2c+bc^2\right)+\left(ac^2-a^2c\right)-ab\left(a+b\right)\)
\(=bc\left(b+c\right)+ac\left(a-c\right)-ab\left(a+b\right)\)
\(=bc\left(b+c\right)-ac\left(a+c\right)-ab\left(a+b\right)\)
\(=\left(bc-ac-ab\right)\left(b+c+a+c+a+b\right)\)
\(=\left(bc-ac-ab\right)\left(a+b+c\right)^2\)
\(f,x^3-x^2-5x+125\)
\(=\left(x^3+125\right)-x^2-5x\)
\(=x^3+15x^2+75x+125-x^2-5x\)
\(=x^3+14x^2+70x+125\)
mk làm nốt câu cuối nha .
g) ta có : \(x^3+2x^2-6x-27=x^3-3x^2+5x^2-15x+9x-27\)
\(x^2\left(x-3\right)+5x\left(x-3\right)+9\left(x-3\right)=\left(x^2+5x+9\right)\left(x-3\right)\)
