Simplify: (2a + 3b)3 + (2a - 3b)3.
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Answered by
0
Answer:
ANSWER
(2a+3b)
3
=(2a)
3
+(3b)
3
+3(2a)(3b)(2a+3b)
Using, (a+b)
3
=a
3
+b
3
+3ab(a+b)
=8a
3
+27b
3
+18ab(2a+3b)
=8a
3
+27b
3
+36a
2
b+54ab
2
.........(i)
(2a−3b)
3
=(2a)
3
−(3b)
3
−3(2a)(3b)(2a−3b)
Using, (a−b)
3
=a
3
−b
3
−3ab(a−b)
=8a
3
−27b
3
−18ab(2a−3b)
=8a
3
−27b
3
−36a
2
b+54ab
2
......(ii)
Subtracting (i) from (ii) we get,
(2a+3b)
3
−(2a−3b)
3
=8a
3
+27b
3
+36a
2
b+54ab
2
−(8a
3
−27b
3
−36a
2
b+54ab
2
)
=8a
3
+27b
3
+36a
2
b+54ab
2
−8a
3
+27b
3
+36a
2
b−54ab
2
=54b
3
+72a
2
b
Answered by
2
Step-by-step explanation:
=(2a + 3b)3 + (2a - 3b)3
=6a+9b+6a-9b
=(6+6)a+(9-9)b
=12a
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