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.
The sum of cubes formula be used to factor [tex]x^3y^3+343[/tex] is explained below.
A sum of cubes is a two-term expression where both terms are cubes and each term has the same sign. It is factored according to the formula;
[tex]a^3 + b^3 = (a + b) (a^2 - ab + b^2)[/tex]
We have,
[tex]x^3y^3+343[/tex]
Process :
First rewrite [tex]x^3y^3[/tex] as [tex](xy)^3[/tex].
i.e. [tex](xy)^3+343[/tex]
Now, rewrite [tex]343[/tex] in cube form [tex]7^3[/tex],
i.e. [tex](xy)^3+7^3[/tex]
Now, both terms are in perfect cube form,
So, factorized using above given cube formula,
[tex]a^3 + b^3 = (a + b) (a^2 - ab + b^2)[/tex]
[tex](xy)^3+7^3=(xy+7)((xy)^2-(xy)*7+7^2)[/tex]
Now,
[tex](xy)^3+7^3=(xy+7)(x^2y^2-7x)+49)[/tex]
So, this is the process in which sum of cubes formula be used to factor [tex]x^3y^3+343[/tex].
Hence, we can say that the process in which sum of cubes formula be used to factor [tex]x^3y^3+343[/tex] is explained above.
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