Expand (3c + 5)^2
By using a+b = a^2 + b^2 + 2ab
Answers
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Step-by-step explanation:
We know that:
(a+b+c)
3
=a
3
+b
3
+c
3
+3(a+b)(b+c)(a+c)
∴(a−2b+3c)
3
=a
3
+(−2b)
3
+(3c)
3
+3[a+(−2b)][(−2b)+(3c)][(3c)+a]
=a
3
−8b
3
+27c
3
+3(a−2b)(3c−2b)(a+3c)
=a
3
−8b
3
+27c
3
+3[(3ac−2ab−6bc+4b
2
)(a+3c)]
=a
3
−8b
3
+27c
3
+3[3a
2
c−2a
2
b−6abc+4ab
2
+9ac
2
−6abc−18bc
2
+12b
2
c]
=a
3
−8b
3
+27c
3
+9a
2
c−6a
2
b−18abc+12ab
2
+27ac
2
−18abc−54bc
2
+36b
2
c
(a−2b+3c)
3
=a
3
−8b
3
+27c
3
+9a
2
c−6a
2
b+12ab
2
+36cb
2
+27ac
2
−54bc
2
−36abc.
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