Answer:
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.
Step-by-step explanation:
It's the sample response to the problem.
The given expression as a sum of cubes can be written as [tex](xy)^3+7^3[/tex]. And the factors of the given expression will be [tex](xy+7)(x^2y^2+49-7xy)[/tex].
The given expression is [tex]x^3y^3+343[/tex].
It is required to write the expression as sum of cubes.
The first term of the given expression contains x and y variables. And the second term includes 343 which is the cube of 7.
So, the given expression can be written as,
[tex]x^3y^3+343=(xy)^3+7^3[/tex]
So, the given expression can be written as sum of cube of xy and 7.
To factorize the given expression, use the formula [tex]a^3+b^3=(a+b)(a^2+b^2-ab)[/tex] where a is equal to xy and b is equal to 7.
[tex]a^3+b^3=(a+b)(a^2+b^2-ab)\\(xy)^3+7^3=(xy+7)((xy)^2+7^2-7xy)\\(xy)^3+7^3=(xy+7)(x^2y^2+49-7xy)[/tex]
Therefore, the given expression as a sum of cubes can be written as [tex](xy)^3+7^3[/tex]. And the factors of the given expression will be [tex](xy+7)(x^2y^2+49-7xy)[/tex].
For more details, refer to the link:
https://brainly.com/question/21590574
