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Phân tích thành đa nhân tử
đc kết quả :
(2x+1)(3x+1)
:)
5x^2 + 5xy - x - y
=5x.(x+y)-(x+y)
=(x+y)(5x-1)
7x - 6x^2 - 2
=-6x2+3x+4x-2
=-3x.(2x-1)+2.(2x-1)
=(2x-1)(2-3x)
a: Sửa đề: x^3-x^2+5x-5
=x^2(x-1)+5(x-1)
=(x-1)(x^2+5)
b: x^3+4x^2+x-6
=x^3-x^2+5x^2-5x+6x-6
=(x-1)(x^2+5x+6)
=(x-1)(x+2)(x+3)
c: \(=\left(x+2\right)^3+y^3\)
\(=\left(x+2+y\right)\left(x^2+4x+4-xy-2y+y^2\right)\)
\(x^4-6x^3+54x-81\)
\(=x^4+3x^3-9x^3+27x^2-27x^2 +81x-27x-81\)
\(=\left(x^4+3x^3\right)-\left(9x^3+27x^2\right)+\left(27x^2+81x\right)-\left(27+81\right)\)
\(=x^3\left(x+3\right)-9x^2\left(x+3\right)+27x\left(x+3\right)-27\left(x+3\right)\)
\(=\left(x+3\right)\left(x^3-9x^2+27x-27\right)\)
\(=\left(x+3\right)\left(x-3\right)^3\)
\(=6x^3\left(x-2\right)+17x^2\left(x-2\right)-4x\left(x-2\right)-3\left(x-2\right)\)
\(=\left(6x^3+17x^2-4x-3\right)\left(x-2\right)\)
\(=\left[6x^2\left(x+3\right)-x\left(x+3\right)-\left(x+3\right)\right]\left(x-2\right)\)
\(=\left(x-2\right)\left(x+3\right)\left(6x^2-x-1\right)\)
\(=\left(x-2\right)\left(x+3\right)\left[2x\left(3x+1\right)-\left(3x+1\right)\right]\)
\(=\left(x-2\right)\left(x+3\right)\left(2x-1\right)\left(3x+1\right)\)
\(=6x^2-2x-\left(9x-3\right)\)
\(=2x\left(3x-1\right)-3\left(3x-1\right)\)
\(=\left(2x-3\right)\left(3x-1\right)\)
\(=6x\left(x+2y\right)+5\left(x+2y\right)=\left(6x+5\right)\left(x+2y\right)\)
\(=6x\left(x+2y\right)+5\left(x+2y\right)=\left(x+2y\right)\left(6x+5\right)\)