Question

multitplicacion de polinomios :::::::::::::::::::::::::::::::

calcular P(X).Q(X)

a) P(X)= x³+3x²+1 Q(x)= X+3

b) p(x) = x³+2x²+3x-1 Q(x)= 2X+3

C) P(x) = 3X³+5-6X Q(x)=X²+2

D) P(x)= X²+X+1 Q(x)=X²-X-1

E) P(x)= Z³+2Z²-Z Q(X)= z²-2z+5

f) p(X)= n2-2n+1 Q(x)= n²-1

g) 2a-5a²+a³-3 Q(x)= a³-2a-7

h) p(X)= y²-2y+1 Q(X)= y⁴-2y²+2
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producto de la suma por su diferencia

1) (a²-2a+3)(a²+2a+3)
2) (x-x+z)(x+y-z)
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Answer 1

$a) P(x)= x^3+3x^2+1\qquad Q(x)= x+3 \\ \\ ( x^3+3x^2+1)(x+3)= x^4+3x^3+3x^3+9x^2+x+3 \\ \\ ( x^3+3x^2+1)(x+3)= x^4+6x^3+9x^2+x+3 \\ \\ \\ b) P(x) = x^3+2x^2+3x-1\qquad Q(x)= 2x+3 \\ \\ (x^3+2x^2+3x-1)*(2x+3)=2x^4+3x^3+4x^3+6x^2+6x^2+9x \\.\qquad \qquad \qquad\qquad \qquad \qquad \qquad -2x-3 \\ \\ (x^3+2x^2+3x-1)*(2x+3)=2x^4+7x^3+12x^2+7x-3$

$c) P(x) = 3x^3+5-6x\qquad Q(x)=x^2+2 \\ \\ (3x^3-6x+5)(x^2+2)= 3x^5+6x^3-6x^3-12x+5x^2+10 \\ \\ (3x^3-6x+5)(x^2+2)= 3x^5-12x+5x^2+10 \\ \\ \\ d) P(x)=x^2+x+1\qquad Q(x)=x^2-x-1 \\ \\ (x^2+x+1)(x^2-x-1)= x^4-x^3-x^2+x^3-x^2-x+x^2-x-1 \\ \\ (x^2+x+1)(x^2-x-1)= x^4-x^2-2x-1$

$e) P(z)= z^3+2z^2-z\qquad Q(z)= z^2-2z+5 \\ \\ (z^3+2z^2-z)(z^2-2z+5)= z^5-2z^4+5z^3+2z^4-4z^3+10z^2-z^3 \\ .\qquad\qquad\qquad\qquad \qquad \qquad\quad +2z^2-5z \\ \\ (z^3+2z^2-z)(z^2-2z+5)= z^5+12z^2 -5z \\ \\ \\ f) P(n)= n^2-2n+1 \qquad Q(n)= n^2-1 \\ \\ (n^2-2n+1)(n^2-1)=n^4-n^2-2n^3+2n+n^2-1 \\ \\ (n^2-2n+1)(n^2-1)=n^4-2n^3+2n-1$

$g)P(a)= 2a-5a^2+a^3-3\qquad Q(a)= a^3-2a-7 \\ \\ (a^3-5a^2+2a-3)(a^3-2a-7)=a^6-2a^4-7a^3-5a^5+10a^3+35a^2 \\ .\qquad\qquad\qquad\qquad\qquad \qquad \qquad +2a^4-4a^2-14a-3a^3+6a+21 \\ \\ (a^3-5a^2+2a-3)(a^3-2a-7)=a^6-5a^5+31a^2-8a+21 \\ \\ \\ h) P(y)= y^2-2y+1 \qquad Q(y)= y^4-2y^2+2 \\ \\ (y^2-2y+1)( y^4-2y^2+2)=y^6-2y^4+2y^2-2y^5+2y^3-4y \\ .\qquad\qquad\qquad\qquad\qquad \qquad \qquad + y^4 -2y^2+2 \\ \\ (y^2-2y+1)( y^4-2y^2+2)=y^6-2y^5-y^4+2y^3-4y +2$


$1) (a^2-2a+3)(a^2+2a+3)=a^4+2a^3+3a^2-2a^3-4a^2-6a+3a^2 \\.\qquad \qquad \qquad\qquad \qquad \qquad \qquad +6a+9 \\ \\ (a^2-2a+3)(a^2+2a+3)=a^4+3a^2+2a^2+9 \\ \\ \\ 2) (x-y+z)(x+y-z)=x^2+xy-xz-yx-y^2+yz+zx+zy-z^2 \\ \\ (x-y+z)(x+y-z)=x^2-y^2+2yz-z^2$

Espero que te sirva, salu2!!!!