Toán Lớp 8: a) y-x^2y-2xy^2-y^3 b) x^2-25+y^2+2xy c) (x+y)^2-(x^2y) d) x^2+4x-y^2+4 e) 2xy-x^2-y^2+16

Question

Toán Lớp 8:  a) y-x^2y-2xy^2-y^3 b) x^2-25+y^2+2xy c) (x+y)^2-(x^2y) d) x^2+4x-y^2+4 e) 2xy-x^2-y^2+16

phuongthuydung · Answer

a, y - x^2 y - 2xy^2 - y^3   = y(1 - x^2 - 2xy - y^2 )   =y[1 -(x^2 + 2xy +y^2 )]   = y[ 1 - (x+y)^2]   = y(1+x+y)(1-x-y)   b, x^2 - 25 + y^2 + 2xy   =(x^2 + 2xy+y^2) -25   =(x+y)^2 - 5^2   =(x+y+5)(x+y-5)   c, (x+y)^2 - x^2 y^2   = (x+y)^2 - (xy)^2   = (x+y+xy)(x+y-xy)   d, x^2 - 4x - y^2 +4   =(x^2 - 4x +4)^2 -y^2   =(x-2)^2 -y^2   =(x-2+y)(x-2-y)   e, 2xy - x^2 -y^2 +16   = -( x^2 -2xy +y^2 -16)   =-[(x^2 -2xy +y^2 ) -16]   =-[(x-y)^2 -4^2 ]   =-[(x-y+4)(x-y-4)]

minhtamnguyet88 · Answer

Giải đáp:     a. y-x^2y-2xy^2-y^3   = y(1-x^2-2xy-y^2)   = y[1-(x+y)^2]   = y(1-x-y)(1+x+y)   b. x^2-25+y^2+2xy   = (x+y)^2-25   = (x+y-5)(x+y+5)   c. (x+y)^2-(x^2y^2)   = (x+y-xy)(x+y+xy)   d. x^2+4x-y^2+4   = (x+2)^2-y^2   = (x+2-y)(x+2+y)   e. 2xy-x^2-y^2+16   = -(x+y)^2+16   = 4^2-(x+y)^2   = (4-x-y)(4+x+y)