Bài 1: Phân tích đa thức thành nhân tử 1) 2x – 10y 2) 6xy – 8y² 3) 2xy² – 5xy + 4x²y 4) x (x-y) + 2 (x-y) 5) 2x (x-3) + 3 (3-

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1. Giải đáp:

    

   Lời giải và giải thích chi tiết:

   1) 2x – 10y= 2(x-5y)

   2) 6xy – 8y²= 2y(3x-4y)

   3) 2xy² – 5xy + 4x²y=xy(2y-5+4x)

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

   5) 2x (x-3) + 3 (3-x)= 2x(x-3)-3(x-3)=(x-3)(2x-3)

   6) x (x+2) + 3x + 6=x(x+2)+3(x+2)=(x+2)(x+3)

   7) x (x-3) – 2x + 6=x(x-3)-2(x-3)=(x-3)(x-2)

   8) x² – 4y²=x^2-(2y)^2=(x-2y)(x+2y)

   9) 4x² – 25=(2x)^2-5^2=(2x-5)(2x+5)

   10) x² – 12x + 36=x^2-2.x.6+6^2=(x-6)^2

   11) 9x² – 6x + 1=(3x)^2-2.3x.1+1^2=(3x-1)^2

   12) x² + 6x + 9 – y² =x^2+2.x.3+3^2-y^2=(x+3)^2-y^2=(x+3-y)(x+3+y)

   13) x² – 4x + 4 -y²= x^2-2.x.2+2^2-y^2=(x-2)^2-y^2=(x-2-y)(x-2+y)

   14) x² – 9 – 6xy + 9y²=(x^2-6xy+9y^2)-3^2=[x^2-2.x.3y+(3y)^2]-3^2=(x-3y)^2-3^2

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

   15) 3x² – y² – 4y – 4=3x^2-(y^2+4y+4)=3x^2-(y^2+2.y.2+2^2)=3x^2-(y+2)^2=3.(x-y-2)(x+y-2)

   Trả lời
2. Giải đáp:

   1) 2x – 10y= 2(x-5y)

   2) 6xy – 8y²= 2y(3x-4y)

   3) 2xy² – 5xy + 4x²y=xy(2y-5+4x)

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

   5) 2x (x-3) + 3 (3-x)= 2x(x-3)-3(x-3)=(x-3)(2x-3)

   6) x (x+2) + 3x + 6=x(x+2)+3(x+2)=(x+2)(x+3)

   7) x (x-3) – 2x + 6=x(x-3)-2(x-3)=(x-3)(x-2)

   8) x² – 4y²=x^2-(2y)^2=(x-2y)(x+2y)

   9) 4x² – 25=(2x)^2-5^2=(2x-5)(2x+5)

   10) x² – 12x + 36=x^2-2.x.6+6^2=(x-6)^2

   11) 9x² – 6x + 1=(3x)^2-2.3x.1+1^2=(3x-1)^2

   12) x² + 6x + 9 – y² =x^2+2.x.3+3^2-y^2=(x+3)^2-y^2=(x+3-y)(x+3+y)

   13) x² – 4x + 4 -y²= x^2-2.x.2+2^2-y^2=(x-2)^2-y^2=(x-2-y)(x-2+y)

   14) x² – 9 – 6xy + 9y²=(x^2-6xy+9y^2)-3^2=[x^2-2.x.3y+(3y)^2]-3^2=(x-3y)^2-3^2

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

   15) 3x² – y² – 4y – 4=3x^2-(y^2+4y+4)=3x^2-(y^2+2.y.2+2^2)=3x^2-(y+2)^2=3.(x-y-2)(x+y-2)

   Trả lời