Buna seara!
Va rog, ma puteti ajuta putin ?
Imi poate explica cineva ce formule de calcul prescurtat pot folosi? nu imi dau seama ,nu stiu cum sa rezolv logic
Răspunsuri la întrebare
Răspuns:
Explicație pas cu pas:
a) (x-y)(x³+x²y+xy²+y³) = (x⁴+x³y+x²y²+xy³-x³y-x²y²-xy³-y⁴) = x⁴-y⁴
b) (x-1)(x³+x²+x+1) = x⁴+x³+x²+x-x³-x²-x-1 = x⁴-1
c) (x-y)(x⁴+x³y+x²y²+xy³+y⁴) = x⁵+x⁴y+x³y²+x²y³+xy⁴-x⁴y-x³y²-xy⁴-y⁵= x⁵-y⁵
d) (x-2)(x⁴+2x³+4x²+8x+16) = x⁵+2x⁴+4x³+8x²+16x-2x⁴-4x³-8x²-16x-32 =
= x⁵-32
e) (x-y)(x⁵+x⁴y+x³y²+x²y³+xy⁴+y⁵) = x⁶+x⁵y+x⁴y²+x³y³+x²y⁴+xy⁵-
-x⁵y-x⁴y²-x³y³-x²y⁴-xy⁵-y⁶) = x⁶-y⁶
f) (x-1)(x⁵+x⁴+x³+x²+x+1) = x⁶+x⁵+x⁴+x³+x²+x-x⁵-x⁴-x³-x²-x-1 = x⁶-1
g) (x+y)(x⁴-x³y+x²y²-xy³+y⁴) = x⁵-x⁴y+x³y²-x²y³+xy⁴+x⁴y-x³y²+x²y³-xy⁴+y⁵=
= x⁵+y⁵
h) (x+3)(x⁴-3x³+9x²-27x+81) =
= x⁵-3x⁴+9x³-27x²+81x+3x⁴-9x³+27x²-81x+243 = x⁵+243
i) (x+y)(x⁶-x⁵y+x⁴y²-x³y³+x²y⁴-xy⁵+y⁶) =
= x⁷-x⁶y+x⁵y²-x⁴y³+x³y⁴-x²y⁵+xy⁶+x⁶y-x⁵y²+x⁴y³-x³y⁴+x²y⁵-xy⁶+y⁷ = x⁷+y⁷
j) (x+1)(x⁶-x⁵+x⁴-x³+x²-x+1) =
= x⁷-x⁶+x⁵-x⁴+x³-x²+x+x⁶-x⁵+x⁴-x³+x²-x+1 = x⁷+1