Môn Toán Lớp 8: RÚT GỌN a,(3x-1)(9x23x1)12-27 x3 b,(x3)(x-3)-(x5)2 c,(x3)3-(x-3)3

Question

Môn Toán Lớp 8:  RÚT GỌN a,(3x-1)(9x^2+3x+1)+12-27 x^3 b,(x+3)(x-3)-(x+5)^2 c,(x+3)^3-(x-3)^3

doanthulan · Answer

Giải đáp:   a)   (3x-1)(9x^2+3x+1)+12-27x^3   =(3x)^3-1^3+12-27x^3   =27x^3-1+12-27x^3   =(27x^3-27x^3)+(12-1)   =11   b)   (x+3)(x-3)-(x+5)^2   =(x^2-9)-(x^2+10x+25)   =x^2-9-x^2-10x-25   =(x^2-x^2)-10x-(9+25)   =-10x-34   c)   (x+3)^3-(x-3)^3   =x^3+9x^2+27x+27-(x^3-9x^2+27x-27)   =x^3+9x^2+27x+27-x^3+9x^2-27x+27   =(x^3-x^3)+(9x^2+9x^2)+(27x-27x)+(27+27)   =18x^2+54

minhhaanh · Answer

Giải đáp:

a)

$(3x-1).(9x^2+3x+1)+12-27x^{3}$

$= (3x-1).[(3x)^{2}+3x.1+1^2]+12-27x^3$

$= [(3x)^3-1]+12-27x^3$

$= 27x^{3}-1+12-27x^3$

$= (27x^3-27x^3)+(12-1)$
$=11$

b)

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

$=x^2-9-(x^2+10x+25)$

$= x^2-9-x^2-10x-25$

$=(x^2-x^2)-10x-(9+25)$

$= -10x-34$

c)

$(x+3)^{3}-(x-3)^3$

$= x^3+9x^2+27x+27-(x^3-9x^2+27x-27)$

$= x^3+9x^2+27x+27-x^3+9x^2-27x+27$

$= (x^3-x^3)+(9x^2+9x^2)+(27x-27x)+(27+27)$

$= 18x^2+54$

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