Answer:
The factored form is [tex]8x^9-27y^{15}=(2x^3-3y^5)(4x^6+6x^3y^5+9y^{10}[/tex]
Step-by-step explanation:
Given : Expression [tex]8x^9-27y^{15}[/tex]
To find : Factor the expression ?
Solution :
Re-write expression as
[tex]8x^9-27y^{15}=(2x^3)^3-(3y^5)^3[/tex]
Applying identity, [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
Here, [tex]a=2x^3[/tex] and [tex]b=3y^5[/tex]
[tex]8x^9-27y^{15}=(2x^3-3y^5)((2x^3)^2)+(2x^3)(3y^5)+(3y^5)^2[/tex]
[tex]8x^9-27y^{15}=(2x^3-3y^5)(4x^6+6x^3y^5+9y^{10}[/tex]
Therefore, The factored form is [tex]8x^9-27y^{15}=(2x^3-3y^5)(4x^6+6x^3y^5+9y^{10}[/tex]
