Simplify the given expression.
(2.3)
2
+(15.9)
2
+(3.7)
2
−2.3×15.9−15.9×3.7−3.7×2.3
(2.3)
3
+(15.9)
3
+(3.7)
3
−3×2.3×15.9×3.7
- A14.5
- B20.9
- C17.6
- D21.9
Solution & Step-by-step Explanation
Let a=2.3, b=15.9, and c=3.7.
The expression can be rewritten in algebraic form as:
a
2
+b
2
+c
2
−ab−bc−ca
a
3
+b
3
+c
3
−3abc
We know the standard algebraic identity:
a
3
+b
3
+c
3
−3abc=(a+b+c)(a
2
+b
2
+c
2
−ab−bc−ca)
Substituting this identity into the numerator of our expression:
a
2
+b
2
+c
2
−ab−bc−ca
(a+b+c)(a
2
+b
2
+c
2
−ab−bc−ca)
=a+b+c
Now, substitute the values of a, b, and c:
Value=2.3+15.9+3.7=21.9
The expression can be rewritten in algebraic form as:
a
2
+b
2
+c
2
−ab−bc−ca
a
3
+b
3
+c
3
−3abc
We know the standard algebraic identity:
a
3
+b
3
+c
3
−3abc=(a+b+c)(a
2
+b
2
+c
2
−ab−bc−ca)
Substituting this identity into the numerator of our expression:
a
2
+b
2
+c
2
−ab−bc−ca
(a+b+c)(a
2
+b
2
+c
2
−ab−bc−ca)
=a+b+c
Now, substitute the values of a, b, and c:
Value=2.3+15.9+3.7=21.9