Question

rozłożyć działania na czynniki: a) 1+6x+12x^2 + 8x^3 = b) 36p^4 + 12p^2q^2 + q^4 =

Answer 1

a)

1 + 6x + 12 x^2 + 8 x^3 = 8 x^3 + 12 x^2 + 6 x + 1 = ( 2 x + 1)^3

Korzystamy z wzoru;

(a + b)^3 = a^3 + 3 a^2 b + 3 a b^2 + b^3

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a = 2x 

b = 1

b)

36 p^4 + 12 p^2 q^2 +  q^4 = ( 6 p^2 + q^2)^2

Korzystamy z wzoru

( a + b)^2 = a^2 + 2 a b + b^2

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a = 6 p^2

b = q^2