El lenguaje algebraico soluciones

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Soluciones a “Ejercicios y problemas” PÁGINA 87 13

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Opera y simplifica. a) (2x 2 + 3)(x – 1) – x (x – 2) b) (x 2 – 5x + 3)(x 2 – x) – x (x 3 – 3)

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c) 1 x 2 + 5 x + 1 (6x – 12) 2 3 6 a) (2x 2 + 3)(x – 1) – x(x – 2) = 2x 3 – 2x 2 + 3x – 3 – x 2 + 2x = 2x 3 – 3x 2 + 5x – 3 b) (x 2 – 5x + 3)(x 2 – x) – x (x 3 – 3) = x 4 – x 3 – 5x 3 + 5x 2 + 3x 2 – 3x – x 4 + 3x = = –6x 3 + 8x 2

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c) 1 x 2 + 5 x + 1 (6x – 12) = 3x 3 – 6x 2 + 10x 2 – 20x + x – 2 = 2 3 6 = 3x 3 + 4x 2 – 19x – 2 14

Extrae factor común. a) 12x 3 – 8x 2 – 4x b) –3x 3 + x – x 2 c) 2xy 2 – 4x 2y + x 2y 2 d) 2 x 2 + 1 x 3 – 5 x 3 3 3 a) 12x 3 – 8x 2 – 4x = 4x (3x 2 – 2x – 1) b) –3x 3 + x – x 2 = x (–3x 2 + 1 – x) c) 2xy 2 – 4x 2y + x 2y 2 = xy (2y – 4x + xy) d) 2 x 2 + 1 x 3 – 5 x = 1 x (2x + x 2 – 5) 3 3 3 3

Identidades notables 15

Desarrolla estas expresiones: a) (x + 6)2 c) (3x – 2)2 e) (x – 2y )2

b) (7 – x)2 2 d) x + 1 2 f) 2 x – 1 y 5 3

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a) (x + 6)2 = x 2 + 36 + 12x

b) (7 – x)2 = 49 + x 2 – 14x

c) (3x – 2)2 = 9x 2 + 4 – 12x

d) x + 1 2

e) (x – 2y)2 = x 2 + 4y 2 – 4xy

Unidad 4. El lenguaje algebraico

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( ) = x + 14 + x f) ( 2 x – 1 y) = 4 x + 1 y 5 3 25 9 2

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– 4 xy 15


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