Ejercicios Matematicas
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Publicado: 20 de enero de 2013
UNIVERSIDAD DE SAN CARLOS DE GUATEMALA
FACULTAD DE CIENCIAS ECONÓMICAS
ÁREA COMÚN
CURSO DE MATEMÁTICA I
HOJA DE EJERCICIOS DE PRODUCTOS NOTABLES
1.
(x+8)2
=
(x)2+2(x)(8)+(8)2
=x2+16x+64
2.
(x2-9)2
=
(x2)2+2(x2)(9)+(9)2
=
x4-18x2+81
3.
(5x3-4y2)2
=
(5x3)2+2(5x3)(4y2)+(4y2)2
=
25x6+40x3y2+16y4
4.
(7x-4)2
=(7x)2+2(7x)(4)+(4)2
=
49x2+56x+16
5.
(a3+2x4)(a3+2x4)
=
(a3+2x4)2
=
6.
(2x2-y3)2
=
(2x2)2-2(2x2)(y3)+(y3)2
=
4x4-4x2y3+y6
7.
(4a5+3)2
=
(4a5)2+2(4a5)(3)+(3)2
=16a10+24a5+9
8.
(x+y)(x_y)
=
(x)(x)-(y)(y)
=
x2-y2
9.
(6x-5y)(6x+5y)
=
(6x)(6x)-(5y)(5y)
=
36x2-25y2
10. (2x3+7y2)(2x3-7y2)
=
(2x3)(2x3)-(7y2)(7y2)=
4x6-49y4
11. (x+3y+2z)(x+3y-2z)
=
[(x+3y)+2z][(x+3y)-2z]
=
(x+3y)2-4z2
=
x2+6xy+9y2-4z2
12. (x+y+3z)(x-y-3z)
=
[x+(y+3z)][x-(y+3z)]
=
x2-(y+3z)2
=x2-y2-6yz-9z2
13. (4x+3y-2z)(4x-3y+2z)
=
[4x+(3y-2z)][4x-(3y-2z)]=
16x2-(3y-2z)2
=
16x2-9y2+12yz-4z2
14. (x2-3x+4)(x2+3x+4)
=
[(x2+4)-3x][(x2+4)+3x]
=
(x2+4)2-9x2
==
x4+8x2+16-9x2
x4-x2+16
15. (4x2-2x-3)(4x2+2x-3)
=
[(4x2-3)-2x][(4x2-3)+2x]
=
(4x2-3)2-4x2
=
=
16x4-24x2+9-4x2
16x4-28x2+9
16. (x2-xy+y2)(x2+y2+xy)
=[(x2+y2)-xy][(x2+y2)+xy]
=
(x2+y2)2-x2y2
=
=
x4+2x2y2+y4-x2y2
x4+x2y2+y4
17. (x+y)3
=
(x)3+3(x)2(y)+3(x)(y)2+(y)3
=
x3+3(x2)(y)+3(x)(y2)+y3
=
x3+3x2y+3xy2+y3
18. (x-y)3=
(x)3-3(x)2(y)+3(x)(y)2-(y)3
=
x3-3(x2)(y)+3(x)(y2)-(y3)
=
x3-3x2y+3xy2-y3
19. (4x+2)3
=
(4x)3+3(4x)2(2)+3(4x)(2)2+(2)3
=
64x3+3(16x2)(2)+3(4x)(4)+8
=64x3+96x2+48x+8
20. (7x+5)3
=
(7x)3+3(7x)2(5)+3(7x)(5)2+(5)3
=
343x3+3(49x2)(5)+3(7x)(25)+125 =
343x3+735x2+525x+125
21. (3x2-2y)3
=
(3x2)3-3(3x2)2(2y)+3(3x2)(2y)2-(2y)3 =...
FACULTAD DE CIENCIAS ECONÓMICAS
ÁREA COMÚN
CURSO DE MATEMÁTICA I
HOJA DE EJERCICIOS DE PRODUCTOS NOTABLES
1.
(x+8)2
=
(x)2+2(x)(8)+(8)2
=x2+16x+64
2.
(x2-9)2
=
(x2)2+2(x2)(9)+(9)2
=
x4-18x2+81
3.
(5x3-4y2)2
=
(5x3)2+2(5x3)(4y2)+(4y2)2
=
25x6+40x3y2+16y4
4.
(7x-4)2
=(7x)2+2(7x)(4)+(4)2
=
49x2+56x+16
5.
(a3+2x4)(a3+2x4)
=
(a3+2x4)2
=
6.
(2x2-y3)2
=
(2x2)2-2(2x2)(y3)+(y3)2
=
4x4-4x2y3+y6
7.
(4a5+3)2
=
(4a5)2+2(4a5)(3)+(3)2
=16a10+24a5+9
8.
(x+y)(x_y)
=
(x)(x)-(y)(y)
=
x2-y2
9.
(6x-5y)(6x+5y)
=
(6x)(6x)-(5y)(5y)
=
36x2-25y2
10. (2x3+7y2)(2x3-7y2)
=
(2x3)(2x3)-(7y2)(7y2)=
4x6-49y4
11. (x+3y+2z)(x+3y-2z)
=
[(x+3y)+2z][(x+3y)-2z]
=
(x+3y)2-4z2
=
x2+6xy+9y2-4z2
12. (x+y+3z)(x-y-3z)
=
[x+(y+3z)][x-(y+3z)]
=
x2-(y+3z)2
=x2-y2-6yz-9z2
13. (4x+3y-2z)(4x-3y+2z)
=
[4x+(3y-2z)][4x-(3y-2z)]=
16x2-(3y-2z)2
=
16x2-9y2+12yz-4z2
14. (x2-3x+4)(x2+3x+4)
=
[(x2+4)-3x][(x2+4)+3x]
=
(x2+4)2-9x2
==
x4+8x2+16-9x2
x4-x2+16
15. (4x2-2x-3)(4x2+2x-3)
=
[(4x2-3)-2x][(4x2-3)+2x]
=
(4x2-3)2-4x2
=
=
16x4-24x2+9-4x2
16x4-28x2+9
16. (x2-xy+y2)(x2+y2+xy)
=[(x2+y2)-xy][(x2+y2)+xy]
=
(x2+y2)2-x2y2
=
=
x4+2x2y2+y4-x2y2
x4+x2y2+y4
17. (x+y)3
=
(x)3+3(x)2(y)+3(x)(y)2+(y)3
=
x3+3(x2)(y)+3(x)(y2)+y3
=
x3+3x2y+3xy2+y3
18. (x-y)3=
(x)3-3(x)2(y)+3(x)(y)2-(y)3
=
x3-3(x2)(y)+3(x)(y2)-(y3)
=
x3-3x2y+3xy2-y3
19. (4x+2)3
=
(4x)3+3(4x)2(2)+3(4x)(2)2+(2)3
=
64x3+3(16x2)(2)+3(4x)(4)+8
=64x3+96x2+48x+8
20. (7x+5)3
=
(7x)3+3(7x)2(5)+3(7x)(5)2+(5)3
=
343x3+3(49x2)(5)+3(7x)(25)+125 =
343x3+735x2+525x+125
21. (3x2-2y)3
=
(3x2)3-3(3x2)2(2y)+3(3x2)(2y)2-(2y)3 =...
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