Odpowiedź:
z.1 a) ( 3 x - 4)² = (3 x)² - 2*3 x*4 + 4² = 9 x² - 24 x + 16
Korzystamy z wzoru: (a - b)² = a² -2 a*b + b²
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b) ( 8 + x )² = 8²+ 2*8*x + x² = 64 + 16 x + x² = x² + 16 x + 64
Korzystamy z wzoru : (a + b)² = a² + 2a*b + b²
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c) Korzystamy z wzoru: (a - b)*( a + b) = a² - b²
( 4 x - 3)*(4 x + 3) = ( 4 x)² - 3² = 16 x² - 9
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d) Korzystamy z wzoru: (a + b)³ = a³ + 3 a²b + 3 a *b² + b³
(a + 2)³ = a³ + 3*a²*2 + 3 a*2² + 2³ = a³ + 6 a² + 12 a + 8
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e) Korzystamy z wzoru:
(a - b)³ = a³ - 3 a²*b +3 a*b² - b³
( 3 - b)³ = 3³ - 3*3²*b + 3*3*b² - b³ = 27 - 27 b + 9 b² - b³
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z.2 a) - 5*(x + 3) + ( x + 2)*( x - 2) - ( x - 3)² =
= - 5 x - 5*3 + x² - 2² - ( x² - 2*x*3 + 3²) = -5 x - 15 +x² - 4 - x² + 6 x - 9 =
= x - 28
b) ( x + 4)²- 3*( x - 3)*( x + 3) + 4*( 5 -2 x) =
=x² + 2*x*4 + 4² - 3*(x² - 3²) + 20 - 8 x = x² +8 x + 16 -3 x² +27 + 20 - 8 x =
= -2 x² + 63
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Z. 1 a) W(x) + Q(x) = ( 5 x³ -2 x² + 6 x - 1) + ( 7 x² + 8 x - 2) =
= 5 x³ + ( -2 x² + 7 x²) + ( 6 x + 8 x) + (- 1 + 2) =
= 5 x³ + 5 x² +14 x - 3
b) 2 P(x) + 3 Q(x) = 2*(-2 x³ + 4 x + 5) + 3*(7 x² + 8 x - 2) =
= - 4 x³ + 8 x + 10 + 21 x² + 24 x - 6 = -4 x³ +21 x² +32 x + 4
d) 2W(x) - [Q(x) + P(x)] = 2*(5 x³ - 2x² + 6 x -1) - [7 x²+8x -2 + (-2 x³+4x +5)] =
= 10x³ -4x²+12x -2 - [ -2x³ + 7 x² + 12 x + 3 ] =
= 10 x³ -4 x² + 12 x - 2 + 2 x³ - 12 x - 3 = 12 x³ -4 x² - 5
Pozostałe analogicznie.
z.2
a) Wx)*P(x) =( 2 x² - 1)*( x³ + x) = 2x²*x³ + 2 x²*x - 1*x³ -1*x =
= 2 [tex]x^5[/tex] + 2 x³ -x³ -x = 2 [tex]x^5 + x^3 - x[/tex]
b) P(x)*Q(x) = (x³ + x)*(2 x² +3 x -1) =x³*2 x² + x³*3x +x³*(-1) + x*2x² + + x*3x+x*(-1) = 2[tex]x^5 + 3 x^4 - x^3 +2 x^3 + 3 x^2 - x =[/tex] 2[tex]x^5 +3 x^4 + x^3 +3 x^2 - x[/tex]
Szczegółowe wyjaśnienie:
