The factored form of the expression [tex]27x^3+y^6[/tex] is [tex](3x+y^2)(9x2-3xy^2+y^4)[/tex]. The correct answer of the factored expression is option A
Given the expression;
[tex]27x^3+y^6[/tex]
This can be expressed as the sum of cubes
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]
The given expression can also be written as the sum of cubes as shown:
[tex]27x^3+y^6 = (3x)^3+(y^2)^3[/tex]
We can see that:
a = 3x
b = y²
Substituting the given parameters into the formula above;
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)\\(3x)^3+(y^2)^3=(3x+y^2)((3x)^2-3xy^2+(y^2)^2)\\(3x)^3+(y^2)^3=(3x+y^2)(9x2-3xy^2+y^4)\\[/tex]
Hence the factored form of the expression is [tex](3x+y^2)(9x2-3xy^2+y^4)[/tex]
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