Question

Представьте в виде произведения:x^3+y^3;a^3-64;8+y^3;m^3+125n^3

Answer 1

X^3+y^3=(x+y)(x^2-xy+y^2)
a^3-64=a^3-4^3=(a-4)(a^2+4a+16)
8+y^3=2^3+y^3=(2+y)(4-2y+y^2)
m^3+125n^3=m^3+5^3n^3=(m+5n)(m^2-5mn+(5n)^2)

Answer 2

x^3 + y^3

The expression x^3 + y^3 represents the sum of the cubes of two variables, x and y. This can be expanded using the formula for the sum of cubes:

x^3 + y^3 = (x + y)(x^2 - xy + y^2)

So, the expression x^3 + y^3 can be factored as (x + y)(x^2 - xy + y^2).

a^3 - 64

The expression a^3 - 64 represents the difference between the cube of a variable, a, and the cube of 4. This can be simplified using the formula for the difference of cubes:

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

In this case, b is equal to 4. So, the expression a^3 - 64 can be factored as (a - 4)(a^2 + 4a + 16).

8 + y^3

The expression 8 + y^3 represents the sum of 8 and the cube of a variable, y. This expression cannot be factored further.

m^3 + 125n^3

The expression m^3 + 125n^3 represents the sum of the cubes of two variables, m and 5n. This can be expanded using the formula for the sum of cubes:

m^3 + n^3 = (m + 5n)(m^2 - 5mn + 25n^2)

So, the expression m^3 + 125n^3 can be factored as (m + 5n)(m^2 - 5mn + 25n^2).

Please let me know if there's anything else I can help you with!