Answer:
True
Step-by-step explanation:
64x³ + 125
64x³ = (4x)³ ← a perfect cube
125 = 5³ ← a perfect cube
Thus 64x³ + 125 ← is a sum of cubes
It is true that the expression which is given below is a sum of cubes.
The given expression is:
[tex]64x^{3} +125[/tex]
As we can see that there are two terms in it:
one is [tex]64x^{3}[/tex] and the second one is [tex]125[/tex].
So, at first, we will see [tex]64x^{3}[/tex]
[tex]64x^{3}=4^{3} *x^{3}[/tex]
from the above, we can state that [tex]64x^{3}[/tex] is a cube of [tex]4x[/tex].
Now, we will look at [tex]125[/tex].
So, [tex]125=5^{3}[/tex]
Therefore, we can also state that [tex]125[/tex] is a cube of [tex]5[/tex].
Hence, the given statement is true.
The sum of cubes (a3 + b3) formula is expressed as a3 + b3 = (a + b) (a2 - ab + b2).
Sum of cubes:The sum of a cubed of two binomial is equal to the cube of the first term, plus three times the square of the first term by the second term, plus three times the first term by the square of the second term, plus the cube of the second term.
The formula to find the sum of cubes of n natural numbers is S = [n2 (n + 1)2]/4, where n is the count of natural numbers that we take.
Learn more about the sum of cubes, refer to:
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