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8a3 - 36a2b + 54ab2 - 27b3 - 8
= ( 8a3 - 36a2b + 54ab2 - 27b3 ) - 8
= ( 2a - 3b )3 - 23
= ( 2a - 3b - 2 )[ ( 2a - 3b )2 + 2( 2a - 3b ) + 4 ]
= ( 2a - 3b - 2 )( 4a2 - 12ab + 9b2 + 4a - 6b + 4 )
a)\(\left(a^3-b^3\right)+\left(a-b\right)^2\)
\(=\left(a-b\right)\left(a^2+ab+b^2\right)+\left(a-b\right)^2\)
\(\left(a-b\right)\left(a^2+ab+b^2+a-b\right)\)
b) \(\left(8a^3-27b^3\right)-2a\left(4a^2-9b^2\right)\)
\(=\left(2a-3b\right)\left(4a^2+6ab+9b^2\right)-2a\left(2a-3b\right)\left(2a+3b\right)\)
\(=\left(2a-3b\right)\left(4a^2+6ab+9b^2-4a^2-6ab\right)\)
\(=\left(2a-3b\right)\cdot9b^2\)
\(=\left(a-b\right)\left(a^2+ab+b^2\right)+a^2-2ab+b^2\)
= ...........
a^3+b^3+c^3−3abc
=a^3+3ab(a+b)+b^3+c^3−3abc−3ab(a+b)
=(a+b)^3+c^3−3ab(a+b+c)
=(a+b+c)(a^2+2ab+b^2−ab−ac+c^2)−3ab(a+b+c)
=(a+b+c)(a^2+b^2+c^2−ab−bc−ca)
a^3 + b^3 + c^3 - 3abc
= ( a+ b)^3 - 3ab ( a+ b) - 3abc
= ( a+ b +c )^3 - 3 ( a + b ).c(a + b +c ) -3ab (a+ b ) -3abc
= ( a+ b +c)^3 - 3(a+b).c(a+b+c) - 3ab(a+b+c)
= ( a+ b +c )[ ( a + b +c )^2 - 3(a+b).c - 3ab ]
= ( a+ b + c ) [ a^2 + 2ab + b^2 + 2bc+ c^2 +2 ac - 3ac - 3bc - 3ab )
= ( a + b + c)(a^2 + b^2 + c^2 -ab - bc- ca)
Tick đúng nha
\(b.\left(a+b+c\right)^3-a^3-b^3-c^3\)
\(=\left(a+b+c-a\right)\left(3a^2+b^2+c^2+3ab+2bc+3ac\right)-\left(b^3+c^3\right)\)
\(=\left(b+c\right)\left(3a^2+b^2+c^2+3ab+2bc+3ac\right)-\left(b+c\right)\left(b^2-bc+c^2\right)\)
\(=\left(b+c\right)\left(3a^2+b^2+c^2+3ab+2bc+3ac-b^2+bc-c^2\right)\)
\(=\left(b+c\right)\left(3a^2+3ab+3ac+3bc\right)\)
\(=3\left(a+b\right)\left(a+c\right)\left(b+c\right)\)
a ) \(a^3+b^3+c^3-3abc\)
\(=\left(a^3+3a^2b+3ab^2+b^3\right)+c^3-3a^2b-3ab^2-3abc\)
\(=\left(a+b\right)^3+c^3-3ab\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2\right)-3ab\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(a^2+2ab+b^2-ac-bc+c^2-3ab\right)\)
\(=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-ac-bc\right)\)
tìm số tự nhiên nhỏ nhất biết rằng khi chia cho 23 dư 21 khi chia cho 17 dư 16
a. \(x^4+3x^3-9x-9=x^3\left(x+1\right)-9\left(x+1\right)\)\(=\left(x+1\right)\left(x^3-9\right)\)
x9 + 1
= (x3)3 + 13
= (x3 + 1)(x6 - x3 + 1)
= (x + 1)(x2 - x + 1)(x6 - x3 +1)
8a3 - 12a2 + 6a - 1
= (2a)3 - 3(2a)21 + 3 . 2a . 12 - 1
= (2a - 1)3
27a3 - 54a2b + 36ab2 - 8b3
= (3a)3 - 3(3a)22b + 3 . 3a . (2b)2 - (2b)3
= (3a - 2b)3