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a) \(7x^3y-3xyz-21x^2+9z\)
\(=7x^2\left(xy-3\right)-3z\left(xy-3\right)\)
\(=\left(7x^2-3z\right)\left(xy-3\right)\)
b) \(4x^2-2x-y^2-y\)
\(=\left[\left(2x\right)^2-y^2\right]-\left(2x+y\right)\)
\(=\left(2x-y\right)\left(2x+y\right)-\left(2x+y\right)\)
\(=\left(2x+y\right)\left(2x-y-1\right)\)
c) \(9x^2-25y^2-6x+10y\)
\(=\left(3x\right)^2-\left(5y\right)^2-2\left(3x-5y\right)\)
\(=\left(3x-5y\right)\left(3x+5y\right)-2\left(3x-5y\right)\)
\(=\left(3x-5y\right)\left(3x+5y-2\right)\)
d) \(\left(5x-4\right)^2+\left(16-25x^2\right)+\left(5x-4\right)\left(3x+2\right)\)
\(=\left(5x-4\right)\left[\left(5x-4\right)+\left(3x+2\right)\right]+\left(4^2-\left(5x\right)^2\right)\)
\(=\left(5x-4\right)\left(8x-2\right)+\left(4-5x\right)\left(4+5x\right)\)
\(=\left(4-5x\right)\left(2-8x\right)+\left(4-5x\right)\left(4+5x\right)\)
\(=\left(4-5x\right)\left[\left(2-8x\right)+\left(4+5x\right)\right]\)
\(=\left(4-5x\right)\left(6-3x\right)\)
a) \(3x^2-5x-8\)
\(=3x^2+3x-8x-8\)
\(=3x\left(x+1\right)-8\left(x+1\right)\)
\(=\left(x+1\right)\left(3x-8\right)\)
b) \(x^4+6x^3+9x^2-16\)
\(=\left(x^2+3x\right)^2-16\)
\(=\left(x^2+3x-4\right)\left(x^2+3x+4\right)\)
\(=\left(x^2-x+4x-4\right)\left(x^2+3x+4\right)\)
\(=\left[x\left(x-1\right)+4\left(x-1\right)\right]\left(x^2+3x+4\right)\)
\(=\left(x-1\right)\left(x+4\right)\left(x^2+3x+4\right)\)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
a) Hình như phân tích không được
b) \(2x^4+5x^3+13x^2+25x+15\)
\(=x^3+1+2x^4+2x^3+13x^2+13x+12x+12+2+2x^3\)
\(=\left(x^3+1\right)+\left(2x^4+2x^3\right)+\left(13x^2+13x\right)+\left(12x+12\right)+2\left(1+x^3\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)+2x^3\left(x+1\right)+13x\left(x+1\right)+12\left(x+1\right)+2\left(x+1\right)\left(x^2-x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1+2x^3+13x+12+2x^2-2x+2\right)\)
\(=\left(x+1\right)\left(3x^2+10x+15+2x^3\right)\)
\(=\left(x+1\right)\left[x^2\left(2x+3\right)+5\left(2x+3\right)\right]\)
\(=\left(x+1\right)\left(x^2+5\right)\left(2x+3\right)\)
Lời giải:
\((5x-4)^2+(16-25x^2)+(5x-4)(3x+2)\)
\(=(5x-4)^2-[(5x)^2-4^2]+(5x-4)(3x+2)\)
\(=(5x-4)^2-(5x-4)(5x+4)+(5x-4)(3x+2)\)
\(=(5x-4)[(5x-4)-(5x+4)+(3x+2)]\)
\(=(5x-4)(3x-6)=3(5x-4)(x-2)\)