Efectúa las multiplicaciones entre polinomios, a. $$ (2 y+3)\left(y^{2}-3 y+2 ight)= $$ b. $$ \left(a^{2}-3 ight)(2 a+5)= $$ c. $$ (-4 x+3)\left(-\frac{1}{2} x ight)= $$ d. $$ 4 a^{2}+3 a-8 $$ $$ \qquad $$ e. $$ \left(5 b^{3}-2 b^{2}+4 b-3 ight)(b-3)= $$ f. $$ \left(2 x^{2}-1 ight)(x+3)= $$ 1. $$ (3 x-4 y)(3 x+7 y)= $$ k. $$ (5 x-4 y)(2 x+7 y)= $$ 1. $$ -7 m^{2}+8 m $$ h. $$ x^{3}+2 x^{2}-3 x+2 $$ \begin{tabular}{ll} \ $$ imes \quad-6 x $$ & -5 \ \hline \end{tabular} 1. $$ \left(\frac{1}{2} x+7 ight)\left(\frac{4}{7} x-6 ight)= $$ (3x-4) $$ (3 x+7)= $$ g. $$ (-5 x+3)(x-5)(2 x+7)= $$ 1. $$ imes \quad 5 m+3 $$

Question

Efectúa las multiplicaciones entre polinomios, a. $$ (2 y+3)\left(y^{2}-3 y+2ight)= $$ b. $$ \left(a^{2}-3ight)(2 a+5)= $$ c. $$ (-4 x+3)\left(-\frac{1}{2} xight)= $$ d. $$ 4 a^{2}+3 a-8 $$ $$ \qquad $$ e. $$ \left(5 b^{3}-2 b^{2}+4 b-3ight)(b-3)= $$ f. $$ \left(2 x^{2}-1ight)(x+3)= $$ 1. $$ (3 x-4 y)(3 x+7 y)= $$ k. $$ (5 x-4 y)(2 x+7 y)= $$ 1. $$ -7 m^{2}+8 m $$ h. $$ x^{3}+2 x^{2}-3 x+2 $$ \begin{tabular}{ll} \ $$ 	imes \quad-6 x $$ & -5 \ \hline \end{tabular} 1. $$ \left(\frac{1}{2} x+7ight)\left(\frac{4}{7} x-6ight)= $$ (3x-4) $$ (3 x+7)= $$ g. $$ (-5 x+3)(x-5)(2 x+7)= $$ 1. $$ 	imes \quad 5 m+3 $$

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(a^{2}-3ight)\left(2a+5ight)$$
- step1: Apply the distributive property:
  $$a^{2}	imes 2a+a^{2}	imes 5-3	imes 2a-3	imes 5$$
- step2: Multiply the terms:
  $$2a^{3}+5a^{2}-6a-15$$
Expand the expression $$ (5 b^{3}-2 b^{2}+4 b-3)(b-3) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(5b^{3}-2b^{2}+4b-3ight)\left(b-3ight)$$
- step1: Apply the distributive property:
  $$5b^{3}	imes b-5b^{3}	imes 3-2b^{2}	imes b-\left(-2b^{2}	imes 3ight)+4b	imes b-4b	imes 3-3b-\left(-3	imes 3ight)$$
- step2: Multiply the terms:
  $$5b^{4}-15b^{3}-2b^{3}-\left(-6b^{2}ight)+4b^{2}-12b-3b-\left(-9ight)$$
- step3: Remove the parentheses:
  $$5b^{4}-15b^{3}-2b^{3}+6b^{2}+4b^{2}-12b-3b+9$$
- step4: Subtract the terms:
  $$5b^{4}-17b^{3}+10b^{2}-15b+9$$
Expand the expression $$ (-5 x+3)(x-5)(2 x+7) $$
Simplify the expression by following steps:
- step0: Calculate:
  $$\left(-5x+3ight)\left(x-5ight)\left(2x+7ight)$$
- step1: Multiply the terms:
  $$\left(-5x^{2}+28x-15ight)\left(2x+7ight)$$
- step2: Apply the distributive property:
  $$-5x^{2}	imes 2x-5x^{2}	imes 7+28x	imes 2x+28x	imes 7-15	imes 2x-15	imes 7$$
- step3: Multiply the terms:
  $$-10x^{3}-35x^{2}+56x^{2}+196x-30x-105$$
- step4: Add the terms:
  $$-10x^{3}+21x^{2}+166x-105$$
Expand the expression $$ (2 y+3)(y^{2}-3 y+2) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(2y+3ight)\left(y^{2}-3y+2ight)$$
- step1: Apply the distributive property:
  $$2y	imes y^{2}-2y	imes 3y+2y	imes 2+3y^{2}-3	imes 3y+3	imes 2$$
- step2: Multiply the terms:
  $$2y^{3}-6y^{2}+4y+3y^{2}-9y+6$$
- step3: Add the terms:
  $$2y^{3}-3y^{2}-5y+6$$
Expand the expression $$ (3 x-4 y)(3 x+7 y) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(3x-4yight)\left(3x+7yight)$$
- step1: Apply the distributive property:
  $$3x	imes 3x+3x	imes 7y-4y	imes 3x-4y	imes 7y$$
- step2: Multiply the terms:
  $$9x^{2}+21xy-12yx-28y^{2}$$
- step3: Subtract the terms:
  $$9x^{2}+9xy-28y^{2}$$
Expand the expression $$ (2 x^{2}-1)(x+3) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(2x^{2}-1ight)\left(x+3ight)$$
- step1: Apply the distributive property:
  $$2x^{2}	imes x+2x^{2}	imes 3-x-3$$
- step2: Multiply the terms:
  $$2x^{3}+6x^{2}-x-3$$
Expand the expression $$ (-4 x+3)(-\frac{1}{2} x) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(-4x+3ight)\left(-\frac{1}{2}xight)$$
- step1: Multiply the terms:
  $$-\frac{1}{2}x\left(-4x+3ight)$$
- step2: Apply the distributive property:
  $$-\frac{1}{2}x\left(-4xight)-\frac{1}{2}x	imes 3$$
- step3: Multiply the terms:
  $$2x^{2}-\frac{3}{2}x$$
Expand the expression $$ (5 x-4 y)(2 x+7 y) $$
Simplify the expression by following steps:
- step0: Multiply the terms:
  $$\left(5x-4yight)\left(2x+7yight)$$
- step1: Apply the distributive property:
  $$5x	imes 2x+5x	imes 7y-4y	imes 2x-4y	imes 7y$$
- step2: Multiply the terms:
  $$10x^{2}+35xy-8yx-28y^{2}$$
- step3: Subtract the terms:
  $$10x^{2}+27xy-28y^{2}$$
Aquí están los resultados de las multiplicaciones entre polinomios:

a. $$ (2 y+3)(y^{2}-3 y+2) = 2y^{3}-3y^{2}-5y+6 $$

b. $$ (a^{2}-3)(2 a+5) = 2a^{3}+5a^{2}-6a-15 $$

c. $$ (-4 x+3)\left(-\frac{1}{2} xight) = 2x^{2}-\frac{3}{2}x $$

d. $$ (5 b^{3}-2 b^{2}+4 b-3)(b-3) = 5b^{4}-17b^{3}+10b^{2}-15b+9 $$

e. $$ (2 x^{2}-1)(x+3) = 2x^{3}+6x^{2}-x-3 $$

f. $$ (3 x-4 y)(3 x+7 y) = 9x^{2}+9xy-28y^{2} $$

g. $$ (5 x-4 y)(2 x+7 y) = 10x^{2}+27xy-28y^{2} $$

h. $$ (-5 x+3)(x-5)(2 x+7) = -10x^{3}+21x^{2}+166x-105 $$

Si necesitas más ayuda o más cálculos, ¡hazmelo saber!
a. $$ 2y^{3}-3y^{2}-5y+6 $$ b. $$ 2a^{3}+5a^{2}-6a-15 $$ c. $$ 2x^{2}-\frac{3}{2}x $$ d. $$ 5b^{4}-17b^{3}+10b^{2}-15b+9 $$ e. $$ 2x^{3}+6x^{2}-x-3 $$ f. $$ 9x^{2}+9xy-28y^{2} $$ g. $$ 10x^{2}+27xy-28y^{2} $$ h. $$ -10x^{3}+21x^{2}+166x-105 $$

Efectúa las multiplicaciones entre polinomios,
a.
b.
c.
d.

e.
f.

k.

h.

-5

(3x-4)
g.

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