Simplify (4m + 5n)²+ (5m + 4n)2 + (4m + 5n) (4m-5n)
Answers
Answered by
0
Let's simplify step-by-step.
(4m+5n)^2+(5m+4n)(2)+(4m+5n)(4m−5n)
Distribute:
=16m^2+40mn+25n^2+(5m)(2)+(4n)(2)+(4m)(4m)+(4m)(−5n)+(5n)(4m)+(5n)(−5n)
=16m^2+40mn+25n^2+10m+8n+16m^2+−20mn+20mn+−25n^2
Combine Like Terms:
=16m^2+40mn+25n^2+10m+8n+16m^2+−20mn+20mn+−25n^2
=(16m^2+16m^2)+(40mn+−20mn+20mn)+(25n^2+−25n^2)+(10m)+(8n)
=32m^2+40mn+10m+8n
Answer:
=32m^2+40mn+10m+8n
Answered by
0
Answer:41 m2 +80mn+ 41n2
Step-by-step explanation:Given, (4m+5n)
2
+(5m+4n)
2
.
We know, (a+b)
2
=a
2
+2ab+b
2
.
Then,
(4m+5n)
2
+(5m+4n)
2
=[(4m)
2
+2(4m)(5n)+(5n)
2
]+[(5m)
2
+2(5m)(4n)+(4n)
2
]
=16m
2
+40mn+25n
2
+25m
2
+40mn+16n
2
=41m
2
+80mn+41n
2
.
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