Toán Lớp 8: Tính: a.(x+3y)(x ² – 2xy+y) b.(6x+1) ²+(6x-1) ²-2(36x ²-1) c.(2x^5-5x ³+x ²+3x-1):(x ²-1) d.(x ²-81+y ²-2xy):(x-y-9)

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1. a)

   (x+3y)(x^2 – 2xy + y)

   =  x . x^2 – x . 2xy + x . y + 3y . x^2 – 3y . 2xy + 3y . y

   = x^3 – 2x^2y + xy + 3x^2y – 6xy^2 + 3y^2

   = x^3 + (3x^2y – 2x^2y) + xy – 6xy^2 + 3y^2

   = x^3 + x^2y + xy – 6xy^2 + 3y^2

   b)

   (6x+1)^2 + (6x-1)^2 – 2 (36x^2 – 1)

   = (6x+1)^2 + (6x-1)^2 – 2 (6x-1)(6x+1)

   = [ (6x+1) – (6x-1)]^2

   =  (6x + 1 – 6x + 1)^2

   = 2^2

   = 4

   c)

   (2x^5 – 5x^3 + x^2 + 3x – 1) : (x^2 – 1)

   = [ (2x^5 – 2x^3) – (3x^3 -3x) + (x^2 – 1)] : (x^2 – 1)

   = [ 2x^3 (x^2-1) – 3x (x^2 – 1) + (x^2 -1)] : (x^2-1)

   = (2x^3  -3x +1)(x^2 – 1) : (x^2-1)

   =  2x^3 – 3x + 1

   d)

   (x^2 – 81 + y^2 – 2xy) : (x-y-9)

   = [ (x^2 – 2xy + y^2) – 81] : (x-y-9)

   =  [(x-y)^2 – 9^2 ] : (x-y-9)

   = (x-y+9)(x-y-9) : (x-y-9)

   = x-y+9

    

   Trả lời
2. Hướng dẫn trả lời:

   a) (x + 3y)(x^2 – 2xy + y)

   = xcdot(x^2 – 2xy + y) + 3ycdot(x^2 – 2xy + y)

   = xcdotx^2 + xcdot(- 2xy) + xcdoty + 3ycdotx^2 + 3ycdot(- 2xy) + 3ycdoty

   = x^3 – 2x^2y + xy + 3x^2y – 6xy^2 + 3y^2

   = x^3 + (- 2x^2y + 3x^2y) – 6xy^2 + 3y^2 + xy

   = x^3 + x^2y – 6xy^2 + 3y^2 + xy

   b) (6x + 1)^2 + (6x – 1)^2 – 2cdot(36x^2 – 1)

   = (6x + 1)^2 – 2cdot[(6x)^2 – 1^2] + (6x – 1)^2

   = (6x + 1)^2 – 2cdot(6x + 1)cdot(6x – 1) + (6x – 1)^2

   = [(6x + 1) – (6x – 1)]^2

   = (6x + 1 – 6x + 1)^2

   = [(6x – 6x) + (1 + 1)]^2

   = 2^2

   = 4

   c) (2x^5 – 5x^3 + x^2 + 3x – 1) ÷ (x^2 – 1)

   = (2x^5 – 2x^3 – 3x^3 + 3x + x^2 – 1) ÷ (x^2 – 1)

   = [(2x^5 – 2x^3) – (3x^3 – 3x) + (x^2 – 1)] ÷ (x^2 – 1)

   = [2x^3cdot(x^2 – 1) – 3xcdot(x^2 – 1) + (x^2 – 1)] ÷ (x^2 – 1)

   = (2x^3 – 3x + 1)cdot(x^2 – 1) ÷ (x^2 – 1)

   = 2x^3 – 3x + 1

   d) (x^2 – 81 + y^2 – 2xy) ÷ (x – y – 9)

   = [(x^2 – 2xy + y^2) – 81] ÷ (x – y – 9)

   = [(x – y)^2 – 9^2] ÷ (x – y – 9)

   = [(x – y) + 9]cdot[(x – y) – 9] ÷ (x – y – 9)

   = (x – y + 9)cdot(x – y – 9) ÷ (x – y – 9)

   = (x – y + 9)

   Trả lời