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)

Question

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)

ngocle44 · Answer

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) &divide; (x^2 - 1)   = (2x^5 - 2x^3 - 3x^3 + 3x + x^2 - 1) &divide; (x^2 - 1)   = [(2x^5 - 2x^3) - (3x^3 - 3x) + (x^2 - 1)] &divide; (x^2 - 1)   = [2x^3cdot(x^2 - 1) - 3xcdot(x^2 - 1) + (x^2 - 1)] &divide; (x^2 - 1)   = (2x^3 - 3x + 1)cdot(x^2 - 1) &divide; (x^2 - 1)   = 2x^3 - 3x + 1   d) (x^2 - 81 + y^2 - 2xy) &divide; (x - y - 9)   = [(x^2 - 2xy + y^2) - 81] &divide; (x - y - 9)   = [(x - y)^2 - 9^2] &divide; (x - y - 9)   = [(x - y) + 9]cdot[(x - y) - 9] &divide; (x - y - 9)   = (x - y + 9)cdot(x - y - 9) &divide; (x - y - 9)   = (x - y + 9)

lanngocha · Answer

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

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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