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x2 - 3x - 4
= \(x^2-3x+\frac{9}{4}-\frac{9}{4}-4\)
\(=\left(x^2-3x+\frac{9}{4}\right)-\frac{25}{4}\)
\(=\left(x-\frac{3}{2}\right)^2-\left(\frac{5}{2}\right)^2\)
\(=\left(x-\frac{3}{2}-\frac{5}{2}\right)\left(x-\frac{3}{2}+\frac{5}{2}\right)\)
\(=\left(x-4\right)\left(x+1\right)\)
Bài 1 :
\(x^2-3x-4\)
\(=x^2+x-4x-4\)
\(=x\left(x+1\right)-4\left(x+1\right)\)
\(=\left(x+1\right)\left(x-4\right)\)
\(5x^3-5x=5x\left(x^2-1\right)\)
\(3x^2+5x-3xy-5x=x\left(3x+5\right)-x\left(3y+5\right)=x\left(3x-3y\right)=3x\left(x-y\right)\)
\(2x^2+y^2-3xy+3x-2y+1=0\)
\(2,25x^2-2.1,5.x\left(y-1\right)+\left(y-1\right)^2-0,25x^2=0\)
\(\left(1,5x-y+1\right)^2-\left(0,5x\right)^2=0\)
\(\left(1,5x-y+1-0,5x\right)\left(1,5x-y+1+0,5x\right)=0\)
\(\left(x-y+1\right)\left(2x-y+1\right)=0\)
Đề bài là j thì b tự lm nhé~
\(x^3-3xy^2-2y^3\)
\(=x^3-xy^2-2xy^2-2y^3\)
\(=x\left(x^2-y^2\right)-2y^2\left(x+y\right)\)
\(=x\left(x-y\right)\left(x+y\right)-2y^2\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy-2y^2\right)\)
\(=\left(x+y\right)\left(x^2-2xy+xy-2y^2\right)\)
\(=\left(x+y\right)\left[x\left(x-2y\right)+y\left(x-2y\right)\right]\)
\(=\left(x+y\right)^2\left(x-2y\right)\)
\(x^3-3xy^2-2y^3\)
\(=x^3-xy^2-2xy^2-2y^3\)
\(=x\left(x^2-y^2\right)-2y^2\left(x+y\right)\)
\(=x\left(x-y\right)\left(x+y\right)-2y^2\left(x+y\right)\)
\(=\left(x+y\right)\left[x\left(x+y\right)-2y^2\right]\)
\(=\left(x+y\right)\left(x^2+xy-2y^2\right)\)
\(=\left(x+y\right)\left(x^2+2xy-xy-2y^2\right)\)
\(=\left(x+y\right)\left[x\left(x-2y\right)-y\left(x-2y\right)\right]\)
\(=\left(x-y\right)\left(x-y\right)\left(x-2y\right)\)
\(=\left(x-y\right)^2\left(x-2y\right)\)
Câu 2 nha
\(a,x^4+2x^3+x^2\)
\(=x^2\left(x^2+2x+1\right)\)
\(=x^2\left(x+1\right)^2\)
\(c,x^2-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2+2xy+y^2-1\right)\)
Làm tính nhân
(4x3+3xy2-2y3).(3x2-5xy-6y2)
=12x5+12y5-20x4y-36x2y3-8xy4
Phân tích đa thức thành nhân tử
10x3+5x2y-10x2y-10xy2+5y3
=10x3-5x2y-10xy2+5y3
=5(2x3-x2y-2xy2+y3-)
c) \(x^2+y^2+xz+yz+2xy\)
\(=\left(x+y\right)^2+z\left(x+y\right)\)
\(=\left(x+y\right)\left(x+y+z\right)\)
b) \(x^3+3x^2-3x-1\)
\(=\left(x^3-1\right)+3x\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1\right)+3x\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+4x+1\right)\)
Thiếu y3 nha bạn :
\(x^3-x+3x^2y+3xy^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y-1\right)\left(x+y+1\right)\)