Phân tích
\(a,2x^3-5x^2+8x-3\)
\(b,3x^2-14x^2+4x-3\)
\(c,12x^2+5x-12y^2+12y-10xy-3\)
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a/ 2x^3 -5x^2 + 8x -3
= 2x^3 -x^2 -4x^2 +2x +6x -3
= x^2 .[2x-1] - 2x[2x-1] +3. [2x-1]
= [x^2-2x+3] [2x-1]
b/ 3x^3 - 14x^2 +4x +3
= 3x^3 +x^2 -15 x^2 -5x +9x +3
= x^2 [3x+1] -5.x [3x+1] +3. [3x+1]
= [x^2 -5x+3] [3x+1]
c/ Đặt C = 12x^2 + 5 x -12 y^2 +12y -10xy -3
= -[12y^2+10xy+3-12x^2-5x-12y]
12y^2 + 10xy +3-12x^2-5x-12y = 18xy +12y^2 -6y - 12x^2 -8xy +4x -9x -6y +3
= 6y [3x+2y-1] - 4.x[3x+2y-1] -3.[3x+2y-1]
= [6y-4x-3] [3x+2y-1]
=> C = -[6y-4x-3]. [ 3x+2y-1]
tom lai minh ra
12x2+5x-12y2+12y-10xy-3=12(x+(2y-1)/3)(x-(6y-3)/4)) co dung ko nha.
1) \(x^2-6x+3\)
\(=x^2-6x+9-6\)
\(=\left(x-3\right)^2-6\)
\(=\left(x-3+\sqrt{6}\right)\left(x-3-\sqrt{6}\right)\)
2) \(2m^2+10m+8\)
\(=2m^2+2m+8m+8\)
\(=2m\left(m+1\right)+8\left(m+1\right)\)
\(=\left(2m+8\right)\left(m+1\right)\)
\(=2\left(m+4\right)\left(m+1\right)\)
3) \(9x^2+6x-8\)
\(=\left(9x^2+6x+1\right)-9\)
\(=\left(3x+1\right)^2-9\)
\(=\left(3x+4\right)\left(3x-2\right)\)
4) \(x^3-5x^2-14x\)
\(=x\left(x^2-5x-14\right)\)
\(=x\left(x^2-2x+7x-14\right)\)
\(=x\left[x\left(x-2\right)+7\left(x-2\right)\right]\)
\(=x\left(x+7\right)\left(x-2\right)\)
c, x4+6x3+11x2+6x+1
=x4+6x3+9x2+2x2+6x+1
=x4+9x2+1+6x3+2x2+6x
=(x2)2+(3x)2+12+2.x2.3x+2.x2.1+2.3x.1 (1)
Áp dụng hằng đẳng thức (a+b+c)2=a2+b2+c2+2ab+2ac+2bc
=> (1)=(x2+3x+1)2
Câu a nhé bạn:
a, 3x2−22xy−4x+8y+7y2+1
=3x2-21xy-xy-3x-x+7y+y+7y2+1
=(3x2−21xy−3x)−(xy-7y2-y)−(x-7y-1)
=3x(x−7y−1)−y(x−7y−1)−(x−7y−1)
=(3x−y−1)(x−7y−1)
a) \(2x^3-5x^2+8x-3\)
\(=\left(2x^3-4x^2+6x\right)-\left(x^2-2x+3\right)\)
\(=2x\left(x^2-2x+3\right)-\left(x^2-2x+3\right)\)
\(=\left(2x-1\right)\left(x^2-2x+3\right)\)
b) bn ktra lại đề
c) \(12x^2+5x-12y^2+12y-10xy-3\)
\(=\left(12x^2-18xy+9x\right)+\left(8xy-12y^2+6y\right)-\left(4x-6y+3\right)\)
\(=3x\left(4x-6y+3\right)+2y\left(4x-6y+3\right)-\left(4x-6y+3\right)\)
\(=\left(3x+2y-1\right)\left(4x-6y+3\right)\)
a﴿ 2x − 5x + 8x − 3 = 2x − 4x + 6x − x − 2x + 3 = 2x x − 2x + 3 − x − 2x + 3 = 2x − 1 x − 2x + 3
c﴿ 12x + 5x − 12y + 12y − 10xy − 3
= 12x − 18xy + 9x + 8xy − 12y + 6y − 4x − 6y + 3
= 3x 4x − 6y + 3 + 2y 4x − 6y + 3 − 4x − 6y + 3
= 3x + 2y − 1 4x − 6y + 3 3 2