Question

Calcule:
a) (x-2)²
b) (x²+3)²
c) (x+8).(4x+5)²
d) (x+1).(x-1)
e) (2x²+3x+6).(x+2)
f) {x+6+[4x.(x-2)+6]}

Answer 1

a)
= (x - 2)²
= x² - 2.2x + 4
= x² - 4x + 4

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b) (x²+3)²

= x⁴ + 2.3.x² + 9
= x⁴ + 6x² + 9

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨

c)
= (x + 8).(4x + 5)²

= (x + 8).(16x² + 2.5.4x + 25)

= (x + 8).(16x² + 40x + 25)

= 16x³ + 40x² + 25x + 128x² + 320x + 200

= 16x³ + 168x² + 345x + 200

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨


d)
= (x + 1).(x - 1)
= x² - x + x - 1
= x² - 1

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
e)

= (2x² + 3x + 6).(x + 2)
= 2x³ + 4x² + 3x² + 6x + 6x + 12
= 2x³ + 7x² + 12x + 12

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f)
= {x + 6 + [4x.(x - 2) + 6]}
= {x + 6 + [4x² - 8x + 6]}
= x + 6 + 4x² - 8x + 6
= 4x² - 8x + x + 6 + 6
= 4x² - 7x + 12