The given expression is a sum of two cubes. The factorization of the given expression is [tex](2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex].
Given:
The given identity is, [tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)[/tex].
It is required to factorize [tex]8q^6r^3 + 27s^6t^3[/tex] using the given identity.
The given expression can be written in the form of sum of two cubes as,
[tex]8q^6r^3 + 27s^6t^3=2^3q^6r^3 + 3^3s^6t^3\\=(2q^2r)^3+(3s^2t)^3[/tex]
Here, a and b are [tex]2q^2r[/tex] and [tex]3s^2t[/tex] respectively.
Now, the factorization of the given expression can be one as,
[tex]a^3 + b^3 = (a + b)(a^2 - ab + b^2)\\(2q^2r)^3+(3s^2t)^3=(2q^2r+3s^2t)((2q^2r)^2-(2q^2r)(3s^2t)+(3s^2t)^2)\\=(2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex]
Therefore, the factorization of the given expression is [tex](2q^2r+3s^2t)(4q^4r^2-6q^2rs^2t+9s^4t^2)[/tex].
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https://brainly.com/question/11994048
