Property 3 of cubes states that the sum of cubes of consecutive natural numbers is equal to the square of their sum multiplied by the sum of the cubes of the numbers minus three times the product of the numbers. In mathematical terms:
a³ + b³ + c³ = (a + b + c)(a² + b² + c² - ab - bc - ac)
For the given expression, 5³ + 6³ + 7³, we can apply property 3 as follows:
a = 5
b = 6
c = 7
Substituting these values into the property 3 formula:
Answers & Comments
Answer:
Property 3 of cubes states that the sum of cubes of consecutive natural numbers is equal to the square of their sum multiplied by the sum of the cubes of the numbers minus three times the product of the numbers. In mathematical terms:
a³ + b³ + c³ = (a + b + c)(a² + b² + c² - ab - bc - ac)
For the given expression, 5³ + 6³ + 7³, we can apply property 3 as follows:
a = 5
b = 6
c = 7
Substituting these values into the property 3 formula:
5³ + 6³ + 7³ = (5 + 6 + 7)(5² + 6² + 7² - 5 * 6 - 6 * 7 - 5 * 7)
Calculating the individual terms:
5 + 6 + 7 = 18
5² = 25
6² = 36
7² = 49
5 * 6 = 30
6 * 7 = 42
5 * 7 = 35
Now, we can substitute these values back into the expression:
(5 + 6 + 7)(5² + 6² + 7² - 5 * 6 - 6 * 7 - 5 * 7)
= 18(25 + 36 + 49 - 30 - 42 - 35)
= 18(25 + 36 + 49 - 30 - 42 - 35)
= 18(73 - 107)
= 18(-34)
= -612
Therefore, 5³ + 6³ + 7³ is equal to -612.
Answer:
the answer is 54 5³means multiply it with 3 and I multiplied others with 3 and added them and got the answer 54
Step-by-step explanation:
5³+6³+7³
15+18+21
54