因式分解 (1)16m^3n^2-9mn^3 (2)4(x-y)^3-8x(x-y)^2 (3)10a(x-y)^2-5
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因式分解 (1)16m^3n^2-9mn^3 (2)4(x-y)^3-8x(x-y)^2 (3)10a(x-y)^2-5b(y-x)
(4)-4(x-2y)^2+9(x+y)^2
(5)(x^2-4x)^2+8(x^2-4x)+16
(4)-4(x-2y)^2+9(x+y)^2
(5)(x^2-4x)^2+8(x^2-4x)+16
1 16m^3n^2-9mn^3
=mn(16m²n-9n²)
2 4(x-y)^3-8x(x-y)^2
=4(x-y)^2[(x-y)-2x]
=4(x-y)^2[-y-x]
=-4(x-y)^2(x+y)
3 10a(x-y)^2-5b(y-x)
=10a(x-y)^2+5b(x-y)
=5(x-y)[10a(x-y)+b]
=5(x-y)[10ax-10y+b]
(4)-4(x-2y)^2+9(x+y)^2
=3^2(x+y)^2-2^2(x-2y)^2
=(3x+3y)^2-(2x-4y)^2
=[(3x+3y)-(2x-4y)][(3x+3y)+(2x-4y)]
=(x+7y)(5x-y)
(5)(x^2-4x)^2+8(x^2-4x)+16
=(x^2-4x+4)^2
=[(x-2)²]^2
=(x-2)^4
=mn(16m²n-9n²)
2 4(x-y)^3-8x(x-y)^2
=4(x-y)^2[(x-y)-2x]
=4(x-y)^2[-y-x]
=-4(x-y)^2(x+y)
3 10a(x-y)^2-5b(y-x)
=10a(x-y)^2+5b(x-y)
=5(x-y)[10a(x-y)+b]
=5(x-y)[10ax-10y+b]
(4)-4(x-2y)^2+9(x+y)^2
=3^2(x+y)^2-2^2(x-2y)^2
=(3x+3y)^2-(2x-4y)^2
=[(3x+3y)-(2x-4y)][(3x+3y)+(2x-4y)]
=(x+7y)(5x-y)
(5)(x^2-4x)^2+8(x^2-4x)+16
=(x^2-4x+4)^2
=[(x-2)²]^2
=(x-2)^4
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