Cách làm cho bạn:
Ta có :
a. $(x + 3)(x ^{2}– 3x + 9) – (54 + x ^{3})$
= $(x + 3)(x ^{2}– 3x + 3 ^{2}) - (54 + x ^{3})$
= $x ^{3}+ 3 ^{3}- (54 + x^{3})$
= $x ^{3}+ 27 - 54 - x ^{3}=-27$
Vậy $(x + 3)(x ^{2}– 3x + 9) – (54 + x ^{3})$ = -27.
b. $(2x + y)(4x ^{2}– 2xy + y ^{2}) – (2x – y)(4x ^{2}+ 2xy + y ^{2})$
= $(2x + y)[(2x) ^{2}– 2 . x . y + y ^{2}] – (2x – y)(2x) ^{2}+ 2 . x . y + y ^{2}]$
= $[(2x) ^{3}+ y]^{3}- [(2x) ^{3}- y ^{3}] $
= $(2x) ^{3}+ y ^{3}- (2x) ^{3}+ y ^{3}= 2y ^{3}$
Vậy $(2x + y)(4x ^{2}– 2xy + y ^{2}) – (2x – y)(4x ^{2}+ 2xy + y ^{2})= 2y ^{3}$
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