Question

2. Suma los siguientes polinomios: A = -5y3 +10y2 - 2y4 - 15
B = 17y4 - 2y3 + 26.
a. A + B.
b. A-B.
c. B-A.​

Answer 1

Respuesta:

Explicación paso a paso:

A = $5y^{3} + 10y^{2} - 2y^{4} - 15$

B = $17y^{4} -2y^{3}+26$

a. A + B.

$5y^{3} + 10y^{2} - 2y^{4} - 15 + 17y^{4} -2y^{3} +26$

$= (17y^{4} - 2y^{4} )+(5y^{3}-2y^{3})+(10y^{2} )+(26-15)$

$= 15y^{4}+3y^{3}+10y^{2}+11$

$= y^{2} (15y^{2} +3y+10) + 11$

b. A - B.

$5y^{3} + 10y^{2} - 2y^{4} - 15-(17y^{4} -2y^{3}+26)$

$= 5y^{3} + 10y^{2} - 2y^{4} - 15-17y^{4} +2y^{3}-26$

$= (-17y^{4} -2y^{4})+(5y^{3} +2y^{3})+(10y^{2})+(-15-26)$

$= -19y^{4}+7y^{3}+10y^{2}-41$

$= y^{2} (-19y^{2} +7y+10)-41$

c. B - A.

$17y^{4} -2y^{3}+26 -(5y^{3} + 10y^{2} - 2y^{4} - 15)$

$=17y^{4} -2y^{3}+26 -5y^{3} - 10y^{2} + 2y^{4} + 15$

$=(17y^{4}+ 2y^{4}) + (-2y^{3}-5y^{3} )+(-10y^{2})+(26+15)$

$=19y^{4}-7y^{3}-10y^{2}+41$

$= y^{2} (19y^{2} -7y-10)+41$