Simplificar (a+b) ^2-(a-b) ^2
Answers
Answer:
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Step-by-step explanation:
La expresión simplificada C=(a-b)[(a+b)^2+(a-b)^2+2ab]+2b^3 queda:
C = 2a^3C=2a
3
Simplificación por pasos
\left(a-b\right)\left(\left(a+b\right)^2+\left(a-b\right)^2+2ab\right)+2b^3(a−b)((a+b)
2
+(a−b)
2
+2ab)+2b
3
Expandiendo:
\left(a+b\right)^2:\quad a^2+2ab+b^2(a+b)
2
:a
2
+2ab+b
2
\left(a-b\right)^2:\quad a^2-2ab+b^2(a−b)
2
:a
2
−2ab+b
2
\left(a+b\right)^2+\left(a-b\right)^2+2ab =a^2+2ab+b^2+a^2-2ab+b^2+2ab(a+b)
2
+(a−b)
2
+2ab=a
2
+2ab+b
2
+a
2
−2ab+b
2
+2ab
Simplificando: =2a^2+2ab+2b^2=2a
2
+2ab+2b
2
C = =\left(a-b\right)\left(2a^2+2ab+2b^2\right)+2b^3=(a−b)(2a
2
+2ab+2b
2
)+2b
3
Expandiendo:
\left(a-b\right)\left(2a^2+2ab+2b^2\right)(a−b)(2a
2
+2ab+2b
2
)
=2a^2a+2aab+2ab^2-2a^2b-2abb-2b^2b=2a
2
a+2aab+2ab
2
−2a
2
b−2abb−2b
2
b
Simplificando:
=2a^3-2b^3=2a
3
−2b
3
C= =2a^3-2b^3+2b^3=2a
3
−2b
3
+2b
3
Sumando términos similares
C=2a^32a
3