a) 2x( 3x² - x ) - 4x²( x - x² + 1 ) + ( x - 3x² )x

= 6x³ - 2x² - 4x³ + 4x⁴ - 4x² + x² - 3x³

= 4x⁴ - x³ - 5x²

b) 12x² - 4x( 3x - 5 ) = 2( 5x + 2 )

<=> 12x² - 12x² + 20x = 10x + 4

<=> 20x = 10x + 4

<=> 20x - 10x = 4

<=> 10x = 4

<=> x = 4/10 = 2/5

\(x^3-64x^2=x^2.\left(x-64\right)\)

\(x^3-64x^2=x^2.\left(x-64\right)\)

( x + y )³ - ( x - y )³

= [ ( x + y ) - ( x - y ) ][ ( x + y )² + ( x + y )( x - y ) + ( x - y )² ]

= ( x + y - x + y )( x² + 2xy + y² + x² - y² + x² - 2xy + y² )

= 2y( 3x² + y² )

(x+y)^3-(x-y)^3=(x+y-x+y)[(x+y)^2-2(x+y)(x-y)+(x-y)^2   áp dụng HĐT nhá

                       =2y(x^2+2xy+y^2 -2x^2 + 2y^2 + x^2 -2xy +y^2)

                       = 2y(4y^2)

                      =8y^3

Cái này nak mk đang rút gọn luôn r nhá

A = x² + 5x + 8

= ( x² + 5x + 25/4 ) + 7/4

= ( x + 5/2 )² + 7/4 ≥ 7/4 ∀ x

Dấu "=" xảy ra khi x = -5/2

=> MinA = 7/4 <=> x = -5/2

B = x( x - 6 )

= x² - 6x

= ( x² - 6x + 9 ) - 9

= ( x - 3 )² - 9 ≥ -9 ∀ x

Dấu "=" xảy ra khi x = 3

=> MinB = -9 <=> x = 3

C = ( 2x - 1 )² + ( x + 2 )²

= 4x² - 4x + 1 + x² + 4x + 4

= 5x² + 5 ≥ 5 ∀ x

Dấu "=" xảy ra khi x = 0

=> MinC = 5 <=> x = 0

\(\left(x+y\right)^2-4x^2\)

\(\left(x+y-2x\right)\left(x+y+2x\right)\)

\(\left(y-x\right)\left(3x+y\right)\)

( x + y )² - 4x²

= ( x + y )² - ( 2x )²

= ( x + y - 2x )( x + y + 2x )

= ( y - x )( y + 3x )

1. 2018² - 2017.2019 = 2018² - ( 2018 - 1 )( 2018 + 1 ) = 2018² - ( 2018² - 1² ) = 2018² - 2018² + 1² = 1

2. 2001² = ( 2000 + 1 )² = 2000² + 2.2000.1 + 1² = 4 000 000 + 4000 + 1 = 4 004 001

3. 1999² = ( 2000 - 1 )² = 2000² - 2.2000.1 + 1² = 4 000 000 - 4000 + 1 = 3 996 001

4. 11³ = ( 10 + 1 )³ = 10³ + 3.10².1 + 3.10.1² + 1³ = 1000 + 300 + 30 + 1 = 1331

5. 19³ = ( 20 - 1 )³ = 20³ - 3.20².1 + 3.20.1 - 1³ = 8000 - 1200 + 60 - 1 = 6859

6. 57.63 = ( 60 - 3 )( 60 + 3 ) = 60² - 3² = 3600 - 9 = 3591

7. 95³ + 3.95².5 + 3.95.5² + 5³ = ( 95 + 5 )³ = 100³ = 1 000 000

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