Operaciones con expresiones algebraicas

Efectúa las siguientes multiplicaciones:

(5x-2)⦁(x^3-4x^2+2x-1)

(5x)(x^3 )=5x^4

(5x)(-4x^2 )=〖-20x〗^3

(5x)(2x)=10x^2

(5x)(-1)=-5x

(-2)(x^3 )=-2x^3

(-2)(-4x^2 )=8x^2

(-2)(2x)=-4x

(-2)(-1)=2

5x^4-20x^3+10x^2-5x-2x^3+8x^2-4x+2

-20x^3-2x^3=-22x^3

10x^2+8x^2=18x^2

-5x-4x=-9x

5x^4-22x^3+18x^2-9x+2

(2a-3b+5)⦁(6a-4b+2)

(2a)(6a)=12a^2

(2a)(-4b)=-8ab

(2a)(2)=4a

(-3b)(6a)=-18ba

(-3b)(-4b)=12b^2

(-3b)(2)=-6b

(5)(6a)=30a

(5)(-4b)=-20b

(5)(2)=10

12a^2-8ab+4a-18ba+12b^2-6b+30a-20b+10

4a+30a=34a

-6b-20b=-26

12a^2+34a-26b-8ab-18ba+12b^2+10

(3x-2)⦁(-5x+3)⦁(x+4)

(3x)(-5x)=-15x^2

(3x)(3)=9x

(-2)(-5x)=10x

(-2)(3)=-6

-15x^2+9x+10x-6

(-15x^2+9x+10x-6)(x+4)

(-15x^2 )(x)=-15x^3

(-15x^2 )(4)=-60x^2

(9x)(x)=9x^2

(9x)(4)=36x

(10x)(x)=10x^2

(10x)(4)=40x

(-6)(x)=-6x

(-6)(4)=-24

-15x^3-60x^2+9x^2+36+10x^2+40x-6x-24

-60x^2+10x^2+9x^2=79x^2

40x-6x=34x

36-24=12

-15x^3+79x^2+34x+12

Efectúa las siguientes divisiones de polinomio entre monomio:

(5x^2 y^4-10x^5 y^6+25x^3 y)/5xy

〖xy〗^3-2x^4 y^5+5x^2

(12a^5 b^2-10a^4 b^3+8a^6 b^7-6a^2 b^5)/(2a^2 b^2 )

6a^3-5a^2 b+4a^4 b^5-3b^3

Efectúa las siguientes sumas y restas:

(2a+3b-5ab)+(5a-4b+2ab)-(7a+b-ab)=

2a+3b-5ab+5a-4b+2ab-7a+b-ab

2a+5a-7a=0

3b+b-4b=0

-5ab+2ab-ab=-4ab

-4ab

(x^3-5x^2+3)-(2x^2+3x-7)-(8x+2)=

x^3-5x^2+3-2x^2+3x-7-8x+2

〖-5x〗^2-2x^2=-7x^2

3-7+2=-2

3x-8x=-5

x^3-7x^2-2-5

(2x^2 y-3xy^2+5xy)-(6xy+2x^2 y-3xy^2 )+(5xy^2-3xy-4x^2 y)=

2x^2 y-3xy^2+5xy-6xy+2x^2 y-3xy^2+5〖xy〗^2-3xy-4x^2 y

2x^2 y+2x^2 y-4x^2 y=0

-3xy^2-3xy^2+5xy^2=-1xy^2

5xy-6xy-3xy=-4xy

-1〖xy〗^2-4xy

Efectúa las siguientes multiplicaciones:

(5x-2)⦁(x^3-4x^2+2x-1)

(5x)(x^3 )=5x^4

(5x)(〖-4x〗^2 )=-20x^3

(5x)(2x)=10x^2

(5x)(-1)=-5x

(-2)(x^3 )=-2x^3

(-2)(-4x^2 )=8x^2

(-2)(2x)=-4x

(-2)(-1)=2

5x^4-20x^3+10x^2-5x-2x^3+8x^2-4x+2

-20x^3-2x^3=-22x^3

10x^2+8x^2=18x^2

-5x-4x=-9x

5x^4-22x^3+18x^2-9x

(2a-3b+5)⦁(6a-4b+2)

(2a)(6a)=12a^2

(2a)(-4a)=-8a^2

(2a)(2)=4a

(-3b)(6a)=-18ba

(-3b)(-4b)=12b^2

(-3b)(2)=-6b

(5)(6a)=30a

(5)(-4b)=-20b

(5)(2)=10

12a^2-8a^2+4a-18ba∓12b^2-6b+30a-20b+10

12a^2-8a^2+12b^2=16a^2

4a+30a=34a

-6b-20b=-26b

-18ba+16a^2+34a-26b+10

Efectúa las siguientes divisiones de monomios (indicando si en algún caso el resultado no es un monomio):

(10x^3 y^4 z)/2xyz=

10/2 x^3/x y^4/y z/z

5x^(3-1) y^(4-1) z^(1-1)

5x^2 y^3 z^0

5x^2 y^3

a^0=1 Cualquier cantidad elevada al exponente 0 siempre dará como resultado 1, por lo tanto z^0 es igual a 1.

(3a^5 b^2)/(2a^4 b)=

3/2 ab

(12x^4 a^5 b)/(4xa^2 b^3 )=

3x^(4-1) a^(5-2) b^(1-3)

3x^3 a^3 b^(-2)

(15x^4 y^6 a^3)/(3x^2 y^4 )=

5x^(4-2) y^(6-4) a^3

5x^2 y^2 a^3

Efectúa las siguientes divisiones:

(5x^2 y^4-10x^5 y^6+25x^3 y)/5xy=

xy^3-2x^4 y^5+5x^2

(12a^5 b^2-10a^4 b^3+8a^6 b^7-6a^2 b^5)/(2a^2 b^2 )=

6a^3-5a^2 b+4a^4 b^5-3b^3

Efectúa las siguientes operaciones:

-2x^2 y^5 z⦁(-2xyz)⦁(-5x^8 a)=

(-2)(-2)(-5)=-20x^11 y^6 x^2 a

(-2a^5 b^6 c4)^4=

(-2)(-2)(-2)(-2)=16a^5 b^6 c256

(20m^4 n^5+8m^3 n^4)/(4mn^2 )=

5m^3 n^3+2m^2 n^2

Dados los polinomios P(x)=-7x^4+6x^2+6x+5, Q(x)=-2x^2+2+3x^5 y R(x)=x^3-x^5+3x^2

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