Question

[Tai Nguyen Phu]

Phân tích đa thức thành nhân tử
a)4x^4+4x^3-x^2-x
b)x^6-x^4-9x^3+9x2
c)x^4-4x^3+8X^2-16x+16
d)(xy+4)^2-4(x+y)^2
e)(ab-xy)^2-(bx-ay)^2
f)(x^2+8x-34)^2-(3x^2-8x-2)^2
g)(a+b+c)^2+(a-b+c)^2-4b^2
h)a(b^2-c^2)-b(c^2-a^2)+c(a^2-b^2)
j)a^5+b^5-(a+b)^5
P/S:Mấy chế giải giúp mình ngen,sáng mai đi học rồi (*_*)"

Answer 1

[Nguyễn Lê Phước Thịnh]

a: \(=4x^3\left(x+1\right)-x\left(x+1\right)\)

\(=x\left(x+1\right)\left(4x^2-1\right)\)

\(=x\left(x+1\right)\left(2x-1\right)\left(2x+1\right)\)

b: \(=x^4\left(x^2-1\right)-9x^2\left(x-1\right)\)

\(=x^2\cdot\left(x-1\right)\left[x^2\left(x+1\right)-9\right]\)

\(=x^2\left(x-1\right)\left(x^3+x-9\right)\)

d: \(=\left(xy+4\right)^2-\left(2x+2y\right)^2\)

\(=\left(xy+4-2x-2y\right)\left(xy+4+2x+2y\right)\)

\(=\left[x\left(y-2\right)-2\left(y-2\right)\right]\left[x\left(y+2\right)+2\left(y+2\right)\right]\)

\(=\left(y-2\right)\left(x-2\right)\left(y+2\right)\left(x+2\right)\)

e: \(=\left(ab-xy-bx+ay\right)\left(ab-xy+bx-ay\right)\)

\(=\left[a\left(b+y\right)-x\left(b+y\right)\right]\left[b\left(a+x\right)-y\left(a+x\right)\right]\)

\(=\left(b+y\right)\left(a-x\right)\left(a+x\right)\left(b-y\right)\)