Page 171 - Matemática Primaria / Libro de Área

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c. Identidad de Steven d. Diferencia de cuadrados

2
2
(x + a)(x + b) = x + (a + b)x + ab (a + b)(a – b) = a – b 2
Ejemplos: Ejemplos:
(x + 6)(x + 2) = x + (6 + 2)x + (6)(2) (7n + 4m)(7n – 4m) = (7n) – (4m) 2
2
2
2
2
= x + 8x + 12 = 49n + 16m 2
(x + 7)(x – 3) = x + (7 – 3)x + (7)(–3) (9z + 8)(9z – 8) = (9z) – (8) 2
2
2
2
2
= x + 4x – 21 = 81z – 64
e. Identidades de Legendre f. Suma y diferencia de cubos

2
2
3
2
2
2
(a + b) + (a – b) = 2a + 2b 2 (a + b)(a – ab + b ) = a + b 3
2
3
2
2
2
(a + b) – (a – b) = 4ab (a – b)(a + ab + b ) = a – b 3
Ejemplos: Ejemplos:
(2x + 6y) + (2x – 6y) = 2(2x) + 2(6y) 2 (x + 2)(x – 2x + 4) = (x + 2)[x – (x)(2) + 2 ]
2
2
2
2
2
2
3
2
3
3
= x + 2 = x + 8
= 8x + 72y 2 (m – 4)(m – 4m + 16) = (m – 4)[m – (m)(4) + 4 ]
(2x + 6y) – (2x – 6y) = 4(2x)(6y)
2
2
2
2
2
Álgebra = 48xy = m – 4 = m – 64
3
3
3
Observa y analiza la resolución de los siguientes productos notables.
a.(–9m x + 8mx ) d.(x + y + z) 2
2 2
2 3
=(8mx – 9m x ) =[(x + y) + z] 2
2 3 2
2
=(8mx ) – 2(8mx )(9m x ) + (9m x ) =(x + y) + 2(x + y)(z) + (z) 2
2 3
2 2
2 3 2
2
2
3 5
2 4
4 6
= 64m x – 144m x + 81m x = x + 2xy + y + 2(x + y)(z) + z 2
2
2
2
2
b.(–15x y + xy ) = x + 2xy + y + (2x + 2y)(z) + z 2
3 4
3 2
2
2
=(xy – 15x y ) = x + 2xy + y + 2xz + 2yz + z 2
3
3 4 2
=(xy ) – 2(xy )(15x y ) + (15x y ) e.(3m + 2n + 4p) 2
3 4
3 2
3 4 2
3
2 6
6 8
4 7
= x y – 30x y + 225x y =[(3m + 2n) + 4p] 2
2
c. (4x – 5) 3 =(3m + 2n) + 2(3m + 2n)(4p) + (4p) 2
2
2
=(4x) – 3(4x) (5) + 3(4x)(5) – (5) 3 = (3m) + 2(3m)(2n) + (2n) + 2(3m + 2n)(4p) + (4p) 2
3
2
2
2
2
3
2
= 64x – 3(16x )(5) + (12x)(25) – 125 = 9m + 12mn + 4n + (6m + 4n)(4p) + 16p 2
2
2
2
3
= 64x – 240x + 300x – 125 = 9m + 12mn + 4n + 24mp + 16np + 16p 2
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