a)$(a+b)^{3}$+$(a-b)^{3}$-6$a^{2}$ b
b)$(a+b)^{3}$-$(a-b)^{3}$- 6$a^{2}$ b
c)$(x+2)^{3}$+$(x-2)^{3}$-2x.($x^{2}$+12
d)$(x+1)^{3}$-$(x+1)^{3}$+6.(x+1).(x-1)
a)$(a+b)^{3}$+$(a-b)^{3}$-6$a^{2}$ b
b)$(a+b)^{3}$-$(a-b)^{3}$- 6$a^{2}$ b
c)$(x+2)^{3}$+$(x-2)^{3}$-2x.($x^{2}$+12
d)$(x+1)^{3}$-$(x+1)^{3}$+6.(x+1).(x-1)
a) `(a+b)³+(a-b)³-6a²b`
`= a³+3a²b+3ab²+b³+a³-3a²b+3ab²-b³-6a²b`
`= 2a³-6a²b+6ab²`
b) Giống câu a
c) `(x+2)³+(x-2)³-2x.(x²+12)`
`= x³+6x²+8x+8+x³-6x²+8x-8-x³+2x³-24x`
`= 2x³-8x`
d) `(x+1)³-(x+1)³+6(x+1)(x-1)`
`= x³+2x²+2x+1-x³-2x²+2x-1+6.(x²-1)`
`= 4x+6x²-6`
Đáp án:
Giải thích các bước giải:
a) ( a + b)³ + ( a – b)³ – 6a²b
= ( a + b + a – b)[( a + b)² –
( a + b)( a – b) + ( a – b)² ]- 6a²b
= 2a( a² + 2ab + b² – a² + b² + a²
– 2ab + b²) – 6a²b
= 2a( a² + 3b²) – 6a²b
= 2a³ + 6ab² – 6a²b
b) ( a + b)³ – ( a – b)³ – 6a²b
= ( a + b – a + b)[( a + b)² +
( a – b)( a + b) + ( a – b)² ] – 6a²b
= 2b( a² + 2ab + b² + a² – b² + a²
– 2ab + b²) – 6a²b
= 2b( 3a² + b² ) – 6a²b
= 2b³ + 6a²b – 6a²b
= 2b³
c) ( x +2)³ + ( x – 2)³ – 2x(x² + 12)
= ( x + 2 + x – 2)[( x + 2)² – ( x + 2)
( x – 2) + ( x – 2)² ] – 2x( x² + 12)
= 2x( x² + 4x + 4 – x² + 4 + x² – 4x + 4] – 2x³ – 24x
= 2x(x² + 12) – 2x³ – 24
= 2x³ + 24x – 2x³ – 24x
= 0
d) (x + 1)³ – (x + 1)³ + 6(x + 1)(x -1)
=( x +1 – x – 1)[ ( x +1)² + ( x + 1)
( x + 1) + ( x + 1)² ] + 6( x² – 1)
= 0.[( x + 1)² + ( x +1)² + ( x +1)² ] + 6x² – 6
= 0 + 6x² – 6
= 6x² – 6