Respuesta :
[tex]\bf \textit{difference of cubes}
\\ \quad \\
a^3+b^3 = (a+b)(a^2-ab+b^2)\qquad
(a+b)(a^2-ab+b^2)= a^3+b^3 \\ \quad \\
a^3-b^3 = (a-b)(a^2+ab+b^2)\qquad
(a-b)(a^2+ab+b^2)= a^3-b^3\\\\
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\boxed{64=4^3}\qquad x^3+64\implies x^3+4^3\implies (x+4)(x^2-x4+4^2)
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(x+4)(x^2-4x+16)[/tex]
Answer:
[tex](x+4)(x^2-4x+4^2)[/tex]
Step-by-step explanation:
We have been given an expression [tex]x^3+64[/tex] and we are asked to rewrite our expression using sum of cubes.
Sum of cubes: [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex].
We can rewrite 64 as: [tex]64=(4*4*4)=4^3[/tex]
This means that a = x and b = 4, Upon substituting these values in sum of cubes formula we will get,
[tex]x^3+64=(x+4)(x^2-4x+4^2)[/tex]
[tex]x^3+64=(x+4)(x^2-4x+4^2)[/tex]
Therefore, after rewriting our given expression as sum of cubes we will get: [tex](x+4)(x^2-4x+4^2)[/tex].
