A cube is an expression that has a power of 3
In algebra, the sum and the difference of two cubes are represented as:
[tex]\mathbf{x^3+y^3=(x+y)(x^2-xy+y^2)}[/tex]
[tex]\mathbf{x^3 -y^3=(x - y)(x^2+xy+y^2)}[/tex]
The options are not clear, so I will give instances.
[tex]\mathbf{(a)\ 64 - a^3}[/tex]
To expand, we make use of:
[tex]\mathbf{x^3 -y^3=(x - y)(x^2+xy+y^2)}[/tex]
Express 64 as 4^3
[tex]\mathbf{64 - a^3 = 4^3 - a^3}[/tex]
By comparison:
x = 4, y = a
So, we have:
[tex]\mathbf{64 - a^3 =(4 - a)(4^2+4a+a^2)}[/tex]
[tex]\mathbf{64 - a^3 =(4 - a)(16+4a+a^2)}[/tex]
Hence, the expanded form of [tex]\mathbf{(a)\ 64 - a^3}[/tex] is:
[tex]\mathbf{64 - a^3 =(4 - a)(16+4a+a^2)}[/tex]
[tex]\mathbf{(b)\ 75 - n^3}[/tex]
Rewrite as:
[tex]\mathbf{75 - n^3 = 5^3 - n^3}[/tex]
Expand using: [tex]\mathbf{x^3 -y^3=(x - y)(x^2+xy+y^2)}[/tex]
[tex]\mathbf{75 - n^3 = (5- n)(5^2 + 5n + n^2)}[/tex]
[tex]\mathbf{75 - n^3 = (5- n)(25 + 5n + n^2)}[/tex]
Read more about sums and differences of cubes at:
https://brainly.com/question/17077929
My brain hurt reading the answer above-
Here:
A. 64 + a12b51
B. –t6 + u3v21
C. 8h45 – k15
