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Lukyo
@Lukyo
January 2020
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Simplifique ao máximo a expressão a seguir:
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PauloBarros
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= (x + y)⁴ - 2xy . [ (x + y)² - xy]
= (x + y)².(x + y)² - 2xy. [ x² + 2xy + y² - xy]
= (x² + 2xy + y²).(x² + 2xy + y²) - 2xy.[x² + xy + y²]
= x².x² + x².2xy + x².y² + 2xy.x² + 2xy.2xy + 2xy.y² + y².x² + y².2xy + y².y² - 2xy.x² - 2xy.xy - 2xy.y²
= x⁴ +
2x³y
+
x²y²
+ 2x³y
+ 4x²y²
+ 2xy³
+ x²y²
+ 2xy³ + y⁴
- 2x³y
- 2x²y²
- 2xy³
= x⁴ + 2x³y + 4x²y² + 2xy³ + y⁴
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PauloBarros
Ok. Corrigido!
Comentários
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→ Eu irei desenvolver os fatores e agrupá-los:
→ Ou ainda :
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Lista de comentários
Verified answer
= (x + y)⁴ - 2xy . [ (x + y)² - xy]= (x + y)².(x + y)² - 2xy. [ x² + 2xy + y² - xy]
= (x² + 2xy + y²).(x² + 2xy + y²) - 2xy.[x² + xy + y²]
= x².x² + x².2xy + x².y² + 2xy.x² + 2xy.2xy + 2xy.y² + y².x² + y².2xy + y².y² - 2xy.x² - 2xy.xy - 2xy.y²
= x⁴ + 2x³y + x²y² + 2x³y + 4x²y² + 2xy³ + x²y² + 2xy³ + y⁴ - 2x³y - 2x²y² - 2xy³
= x⁴ + 2x³y + 4x²y² + 2xy³ + y⁴
Verified answer
→ Eu irei desenvolver os fatores e agrupá-los:
→ Ou ainda :