Question

Rút gọn

a) (x+2) .( x+3) - (x-2) .(x+5)

b) (8-5x).(x+2)+4(x-2).(x+1)+2.(x-2).(x+2)+10

c) 4.(x-1).(x+5)-(x+2)(x+5)-3.(x-1).(x+2)

d) (x-1).(x^5 + x^4 + x^3 + x^2 + x + 1)

Answer 1

a) ( x + 2 )( x + 3 ) - ( x - 2 )( x + 5 )

= x² + 5x + 6 - ( x² + 3x - 10 )

= x² + 5x + 6 - x² - 3x + 10

= 2x + 16

b) ( 8 - 5x )( x + 2 ) + 4( x - 2 )( x + 1 ) + 2( x - 2 )( x + 2 ) + 10

= -5x² - 2x + 16 + 4( x² - x - 2 ) + 2( x² - 4 ) + 10

= -5x² - 2x + 16 + 4x² - 4x - 8 + 2x² - 8 + 10

= x² - 6x + 10

c) 4( x - 1 )( x + 5 ) - ( x + 2 )( x + 5 ) - 3( x - 1 )( x + 2 )

= 4( x² + 4x - 5 ) - ( x² + 7x + 10 ) - 3( x² + x - 2 )

= 4x² + 16x - 20 - x² - 7x - 10 - 3x² - 3x + 6

= 6x - 24

d) ( x - 1 )( x⁵ + x⁴ + x³ + x² + x + 1 )

= x⁶ + x⁵ + x⁴ + x³ + x² + x - x⁵ - x⁴ - x³ - x² - x - 1

= x⁶ - 1