Respuesta :
Answer:
see explanation
Step-by-step explanation:
Given that the the difference of cubes is
a³ - b³ = (a - b)(a² + ab + b²)
Given
64[tex]x^{6}[/tex] - 27 ← a difference of cubes
with a = 4x² and b = 3, thus
= (4x²)³ - 3³
= (4x² - 3)(16[tex]x^{4}[/tex] + 12x² + 9) ← in factored form
The required expression (4x^2-3)(16x^4+12x^2+9).
To evaluate 64x^6-27 as a^3-b^3=(a-b)(a^2+ab+b^2).
What is identity?
Cubic identity is given as [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex].
Here,
=64x^6-27
=(4x^2)^3-3^3
Such that, a =4x^2 and b = 3.
Put a and b in [tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex].
[tex](4x^2)^3-3^3=(4x^2-3)(16x^4+12x^2+9).[/tex]
Thus, the required expression (4x^2-3)(16x^4+12x^2+9).
Learn more about identity here:
https://brainly.com/question/9704094
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