a)(3x+1)^2-4(x-2)^2
b)9(2x+3)^2-4(x+1)
c)125x^3+1
d)8x^3-27
e)x^3+6x^2+12x+8
f)1-9x+27x^2-27x^3
a)(3x+1)^2-4(x-2)^2 b)9(2x+3)^2-4(x+1) c)125x^3+1 d)8x^3-27 e)x^3+6x^2+12x+8 f)1-9x+27x^2-27x^3
By Raelynn
By Raelynn
a)(3x+1)^2-4(x-2)^2
b)9(2x+3)^2-4(x+1)
c)125x^3+1
d)8x^3-27
e)x^3+6x^2+12x+8
f)1-9x+27x^2-27x^3
Đáp án:
Giải thích các bước giải:
a) (3x +1)² -4.(x -2)²
=(3x +1)² -(2x -4)²
=(3x +1 +2x -4).(3x +1 -2x +4)
=(5x -3).(x +5)
b)9.(2x +3)² -4.(x +1)²
=(6x +9) -( 2x +2)²
=( 6x +9 +2x +2).(6x +9 -2x -2)
=( 8x +11).( 4x -7)
c)125x³ +1
=(5x+1).( 25x² -5x +1)
d)8x³ -27
=(2x -3).( 4x² -6x +9)
e)x³ +6x² +12x +8
=x³ +3.x².2 +3.x.2² +2³ (hằng đẳng thức số 6)
=(x +2)³
f)1 -9x +27x² -27x³
=1 -3.1².x +1.3.(3x)² +(3x)³ (hằng đẳng thức số 7)
=(1 -3x)³
Đáp án:
a) ( 3x + 1 )^2 – 4(x – 2 )^2
= (3x)^2 + 2.3x.1 + 1^2 – 4 ( x^2 – 2.x.2 + 2^2 )
= 9x^2 + 6x + 1 – 4x^2 + 16x – 16
= 5x^2 + 32 – 15
b) 9( 2x + 3 )^2 – 4( x + 1 )
= 9 [ (2x)^2 + 2.2x.3 + 3^2 ] – 4x -4
= 36x^2 + 108x + 9 – 4x – 4
= 36x^2 + 104x + 5
c) 125x^3 + 1
= ( 5x )^3 + 1
= ( 5x + 1 ) ( 25x^2 – 5x + 1 )
d) 8x^3 – 27
= ( 2x )^3 – 3^3
= ( 2x – 3 )^3 + 3.2x.3 ( 2x – 3 )
e) x^3+ 6x^2+ 12x+ 8
= x^3 + 3.x^2 . 2 + 3.x. 2^2 + 2^3
= ( x + 2 )^3
f) 1- 9x+27x^2-27x^3
= – ( 27x^3 – 27x^2 + 9x -1 )
= – [ (3x)^3 – 3.(3x)^2.1 + 3.3x. 1^2 + 1^3 ]
= – ( 3x – 1 )^3
Xin ctlhn ạ :333
Giải thích các bước giải: