Question

How would the sum of cubes formula be use to factor x^3y^3+343?Explain the process

Answer 1

Explanation:

To factor, first identify the quantities that are being cubed. The first term is the cube of xy, and the constant is the cube of 7. Next, use the formula to write the factors. The first factor is the sum of xy and 7. The second factor has three terms: the square of xy, the negative of 7xy, and the square of 7.

Answer 2

The formula of perfect cubes is given by:

`a ^ 3 + b ^ 3 = (a + b) (a ^ 2 - ab + b ^ 2)`
We have the following expression:

`x ^ 3y ^ 3 + 343`
For this case:

`a ^ 3 = x ^ 3y ^ 3 b ^ 3 = 343`
Therefore, the values a and b are:

`a = (x ^ 3y ^ 3) ^ {(1/3)} = xy b = (343) ^ {(1/3)} = 7`
Substituting values we have:

`(xy + 7) (x ^ 2y ^ 2 - 7xy + 49)`
Answer:
The equivalent expression is:

`(xy + 7) (x ^ 2y ^ 2 - 7xy + 49)`