Bài 2 : phân tích các đa thức sau thành nhân tử
a, x3 - 2x2 + x
\(=x\left(x^2-2x+1\right)\)
\(=x\left(x-1\right)^2\)
b, x2 - 2x - y2 + 1
\(=x^2-2x+1-y^2\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-1-y\right)\left(x-1+y\right)\)
vt mũ hộ mk đuy bạn :
\(x^3-2x^2+x\)
\(=x^3-x^2-x^2+x\)
\(=\left(x^3-x^2\right)-\left(x^2-x\right)\)
\(=x^2\left(x-1\right)-x\left(x-1\right)\)
\(=\left(x^2-x\right)\left(x-1\right)\)
\(b,x^2-2x-y^2+1\)
\(=\left(x^2-2x+1\right)-y^2\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-1+y\right)\left(x-1-y\right)\)
Bài 1 :
a) \(x\left(x^2+5\right)\)
\(=x^3+5x\)
b) \(\left(3x-5\right)\left(2x+1\right)-\left(6x^2-5\right)\)
\(=6x^2-7x-5-6x^2+5\)
\(=-7x\)
c) \(\left(2x+3\right)\left(2x-3\right)-\left(2x+1\right)^2\)
\(=4x^2-9-\left(4x^2+4x+1\right)\)
\(=4x^2-9-4x^2-4x-1\)
\(=-4x-10\)
d) \(\left(2x^4+x^3-3x^2+5x-2\right):\left(x^2-x+1\right)\)
Đặt phép chia như bình thường
Kết quả : \(2x^2+3x-2\)
Bài 2 :
a) \(x^3-2x^2+x\)
\(=x\left(x^2-2x+1\right)\)
\(=x\left(x-1\right)^2\)
Câu 2 :
b) \(x^2-2x-y^2+1\)
\(=\left(x^2-2x+1\right)-y^2\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-y-1\right)\left(x+y-1\right)\)
\(1a,x\left(x^2+5\right)=x^3+5x\)
\(b,\left(3x-5\right)\left(2x+1\right)-\left(6x^2-5\right)\)
\(=\left(6x^2+3x-10x-5\right)-6x^2+5\)
\(=6x^2-7x-5-6x^2+5\)
\(=-7x\)
\(c,\left(2x+3\right)\left(2x-3\right)-\left(2x+1\right)^2\)
\(=\left(2x\right)^2-3^2-\left[\left(2x\right)^2+2.2x+1^2\right]\)
\(=4x^2-9-\left(4x^2+4x+1\right)\)
\(=4x^2-9-4x^2-4x-1\)
\(=-4x-10=-2\left(2x+5\right)\)
Câu d bn tự đặt phép tính rồi làm phép chia
\(2a,x^3-2x^2+x=x\left(x^2-2x+1\right)\)
\(=x\left(x-1\right)^2\)
\(b,x^2-2x-y^2+1=\left(x^2-2x+1\right)-y^2\)
\(=\left(x-1\right)^2-y^2\)
\(=\left(x-y-1\right)\left(x+y-1\right)\)
