599. Упростите выражение двумя способами:
а) (х+1)^ 3- (х - 1)^3;
б) (x+2)^3+(x-2)^3
а) (х+1)^ 3- (х - 1)^3;
б) (x+2)^3+(x-2)^3
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Answers & Comments
Объяснение:
1) (x+1)^3-(x-1)^3=
=(x+1)(x+1)(x+1)-(x-1)(x-1)(x-1)=
=(x^2+2x+1)(x+1)-(x^2-2x+1)(x-1)=
=x^3+2x^2+x+x^2+2x+1-
-(x^3-2x^2+x-x^2+2x-1)=
=x^3+3x^2+3x+1-x^3+3x^2-3x+1=
=6x^2+2
2) (x+2)^3+(x-2)^3=
=(x+2)(x^2+4x+4)+(x-2)(x^2-4x+4)=
=x^3+6x^2+12x+8+x^3-6x^2+12x--8=
=2x^3+24x