Question

Escreva, no caderno da forma mais simples possível, os polinômios abaixo:

a) (x-5) . (x-6) - (x-2) . (x-3)

b) (x+1) . (x+1) + (x+1) . (x-1) + (-x+1)

c) (x³-y³) . (x+y) - (x²+y²) . (x²-y²)

d) -3b . (a-b) - (a+5) . (b-3)

Alguem ajuda ? Pra manhã !!

Answer 1

a) [(x+1)(x-6)]-[(x-2)(x-3)]
(x²-6x+x-6)-(x²-3x-2x+6)
x²-5x-6-x²+3x+2x-6
-x²+x²-5x+5x-6-6
-12

b) [(x+1)(x+1)]+[(x+1)(x-1)]+(-x+1)
(x²+x+x+1)+(x²-x+x-1)+(-x+1)
(x²+2x+1)+(x²-1)+(-x+1)
x²+2x+1+x²-1-x+1
2x²+x+1

c)[(x³-y³)(x+y)]-[(x²+y²)(x²-y²)]
(x⁴+x³y-y³x-y⁴)-(x⁴-x²y²+y²x²-y⁴)
x⁴+x³y-y³x-y⁴-x⁴+x²y²-y²x²+y⁴
-x⁴+x⁴-y⁴+y⁴-x²y²+x²y²+x³y-y³x
x³y-y³x
xy(x²-y²)



d)[-3b(a-b)]-[(a+5)(b-3)]
( -3ab+3b²)-(ab-3a+5b-15)
-3ab+3b²-ab+3a-5b+15
-3ab-ab+3b²+3a-5b+15
-4ab+3b²+3a-5b+15