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jok3333 [9.3K]
3 years ago
14

How would the expression x^3+64 be rewritten using sum off cubes

Mathematics
2 answers:
Mamont248 [21]3 years ago
8 0
\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\\\\
-------------------------------\\\\
\boxed{64=4^3}\qquad x^3+64\implies x^3+4^3\implies (x+4)(x^2-x4+4^2)
\\\\\\
(x+4)(x^2-4x+16)
gogolik [260]3 years ago
3 0

Answer:

(x+4)(x^2-4x+4^2)

Step-by-step explanation:

We have been given an expression x^3+64 and we are asked to rewrite our expression using sum of cubes.

Sum of cubes: a^3+b^3=(a+b)(a^2-ab+b^2).

We can rewrite 64 as: 64=(4*4*4)=4^3

This means that a = x and b = 4, Upon substituting these values in sum of cubes formula we will get,

x^3+64=(x+4)(x^2-4x+4^2)

x^3+64=(x+4)(x^2-4x+4^2)

Therefore, after rewriting our given expression as sum of cubes we will get: (x+4)(x^2-4x+4^2).

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