mình làm được mỗi câu c thoii
\(x^4+4=x^4+4x^2-4x^2+4\)
\(\Leftrightarrow x^4+4x^2+4-4x^2\)
\(\Leftrightarrow\left(x^4+4x^2+4\right)-4x^2\)
\(\Leftrightarrow\left(x^2+2\right)-\left(2x\right)^2\)
\(\Leftrightarrow\left(x^2+2-2x\right)\left(x^2+2+2x\right)\)
bài này mình thêm và bớt 4x2 vào để dễ phân h hơn
b/ \(x^5+x+1=\left(x^5-x^4+x^2\right)+\left(x^4-x^3+x\right)+\left(x^3-x^2+1\right)\)
\(=x^2\left(x^3-x^2+1\right)+x\left(x^3-x^2+1\right)+\left(x^3-x^2+1\right)\)
\(=\left(x^3-x^2+1\right)\left(x^2+x+1\right)\)
a, [ x+y+z]3 - x3 - y3- z3 = x3 + 3x2 [y+z] +3x[y+z]2 + [y+z]3 - x3 - y3 -z3
= 3x2 [y+z] +3x[y+z]2 + y3 +z3 +3yz[y+z] -y3 - z3
= [y+z][ 3x2 +3x[y+z] + 3yz]
= [y+z][ 3x2 +3xy +3xz + 3yz]
= [y+z][ 3x[x+y] +3z[x+y]
= 3[y+z][x+y][x+z]
b, x5 +x +1 = x5 + x4 + x3 + x2 +x +1 - x4 - x3 - x2
= x3 [x2 + x +1] +x2 +x +1 - x2 [ x2 + x +1]
= [x2 +x +1][x3 -x2 +1]
c, x4 + 4 = x4 + 4x2 + 4 - 4x2
= [x2 + 2]2 - [2x]2
= [ x2 + 2x +2][ x2 -2x +2]
bạn có thể tham khao ở đây
https://text.123doc.org/document/3146831-cac-phuong-phap-phan-h-da-thuc-thanh-nhan-tu.htm
hok tốt
d)
\(x\sqrt{x}-x-2x+4\sqrt{x}-2=\left(x\sqrt{x}-x\right)-2\left(x-2\sqrt{x}+1\right)\)
=\(x\left(\sqrt{x}-1\right)-2\left(\sqrt{x}-1\right)^2=\left(\sqrt{x}-1\right)\left(x-2\sqrt{x}+2\right)\)
c) 2x2(x +1) + 4x(x +1); d) 2 x(y - 1) - 2
