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1 mark

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

  1. A
    14.5
  2. B
    20.9
  3. C
    17.6
  4. D
    21.9

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

Practice this question

Try it yourself before checking the explanation above.

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
A
14.5
B
20.9
C
17.6
D
21.9

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