Toán Lớp 8: Phân tích đa thức sau thành nhân tử a) 3x(x + 1) – y(x + 1) b) x² + 5x – xy – 5y c) x² – 4y² – 6x +9 d) 6x² – 7x + 2

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1. a) $3x\left(x+1\right)-y\left(x+1\right)$

   $3x^2+3x-y\left(x+1\right)$

   $=3x^2+3x-xy-y$

   b) $x^2+5x-xy-5y$

   $=\left(x^2+5x\right)+\left(-xy-5y\right)$

   $=x\left(x+5\right)-y\left(x+5\right)$

   $=\left(x+5\right)\left(x-y\right)$

   c) $x^2-4y^2-6x+9$

   $=\left(x-3\right)^2-4y^2$

   $=\left(x-3\right)^2-\left(2y\right)^2$

   $=\left(\left(x-3\right)+2y\right)\left(\left(x-3\right)-2y\right)$

   $=\left(x-3+2y\right)\left(x-3-2y\right)$

   d) $6x^2-7x+2$

   $=\left(6x^2-3x\right)+\left(-4x+2\right)$

   $=3x\left(2x-1\right)-2\left(2x-1\right)$

   $=\left(2x-1\right)\left(3x-2\right)$

   Trả lời
2. a) 3x(x + 1) – y(x + 1)

   =(x+1)(3x-y)

   b) x² + 5x – xy – 5y

   =(x²- xy )+( 5x  – 5y)

   =x(x-y)+5(x-y)

   =(x-y)(x+5)

   c) x² – 4y² – 6x +9

   =(x²- 6x +9) – 4y²

   =(x-3)^2-(2y)^2

   =(x-3-2y)(x-3+2y)

   d) 6x² – 7x + 2

   =6x² – 3x-4x + 2

   =(6x² – 3x)-(4x – 2)

   =3x(2x – 1)-2(2x – 1)

   =(2x-1)(3x-2)

   Trả lời