Express y as the different of two square.
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Answer:
4(x+2y)(2x+y)
=4(2x
2
+xy+4xy+2y
2
)
=4(2x
2
+2y
2
+4xy+xy)
=4(2(x
2
+y
2
+2xy)+xy)
=4(2(x+y)
2
+xy)
=8(x+y)
2
+4xy
=8(x+y)
2
+(x+y)
2
−(x−y)
2
[∵4xy=(x+y)
2
−(x−y)
2
]
=9(x+y)
2
−(x−y)
2
=[3(x+y)]
2
−(x−y)
2
Step-by-step explanation:
4(x+2y)(2x+y)
=4(2x
2
+xy+4xy+2y
2
)
=4(2x
2
+2y
2
+4xy+xy)
=4(2(x
2
+y
2
+2xy)+xy)
=4(2(x+y)
2
+xy)
=8(x+y)
2
+4xy
=8(x+y)
2
+(x+y)
2
−(x−y)
2
[∵4xy=(x+y)
2
−(x−y)
2
]
=9(x+y)
2
−(x−y)
2
=[3(x+y)]
2
−(x−y)
2
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