Bài giải:
a) x3 + 2x2y + xy2– 9x = x(x2 +2xy + y2 – 9)
= x[(x2 + 2xy + y2) – 9]
= x[(x + y)2 – 32]
= x(x + y – 3)(x + y + 3)
b) 2x – 2y – x2 + 2xy – y2 = (2x – 2y) – (x2 – 2xy + y2)
= 2(x – y) – (x – y)2
= (x – y)[2 – (x – y)]
= (x – y)(2 – x + y)
c) x4 – 2x2 = x2(x2 – (√2)2) = x2(x - √2)(x + √2).
a) x3 + 2x2y + xy2– 9x = x(x2 +2xy + y2 – 9)
= x[(x2 + 2xy + y2) – 9]
= x[(x + y)2 – 32]
= x(x + y – 3)(x + y + 3)
b) 2x – 2y – x2 + 2xy – y2 = (2x – 2y) – (x2 – 2xy + y2)
= 2(x – y) – (x – y)2
= (x – y)[2 – (x – y)]
= (x – y)(2 – x + y)
c) x4 – 2x2 = x2(x2 – (√2)2) = x2(x - √2)(x + √2).
a)\(x^3+2x^2y+xy^2-9x\)
\(=x\left(x^2+2xy+y^2-9\right)\)
\(=x\left[\left(x+y\right)^2-3^2\right]\)
\(=x\left(x+y-3\right)\left(x+y+3\right)\)
b)\(2x-2y-x^2+2xy+y^2\)
\(=\left(2x-2y\right)-\left(x^2+2xy+y^2\right)\)
\(=2\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(x-y\right)\left[2-\left(x-y\right)\right]\)
\(=\left(x-y\right)\left(2-x+y\right)\)
c)\(x^4-2x^2\)
\(=x^2\left(x^2-2\right)\)
\(=x^2\left[x^2-\left(\sqrt{2}\right)^2\right]\)
\(=x^2\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\)
a) x3+2x2y+xy2-9x
=x.[(x2+2xy+y2)-9]
=x.[(x+y)2-32]
=x.(x+y-3).(x+y+3)
b) 2x-2y-x2+2xy-y2
=(2x-2y)-(x2-2xy+y2)
=2.(x-y)-(x-y)2
=(x-y).(2-x-y)
c) x4-2x2
=x2.(x2-2)