Question

Choose the expressions that are sums or differences of two cubes. 64 a12b51 –t6 u3v21 8h45 – k15 75 – n3p6 –27 – xz9

Answer 1

A cube is an expression that has a power of 3

In algebra, the sum and the difference of two cubes are represented as:

$\mathbf{x^3+y^3=(x+y)(x^2-xy+y^2)}$

$\mathbf{x^3 -y^3=(x - y)(x^2+xy+y^2)}$

The options are not clear, so I will give instances.

$\mathbf{(a)\ 64 - a^3}$

To expand, we make use of:

$\mathbf{x^3 -y^3=(x - y)(x^2+xy+y^2)}$

Express 64 as 4^3

$\mathbf{64 - a^3 = 4^3 - a^3}$

By comparison:

x = 4, y = a

So, we have:

$\mathbf{64 - a^3 =(4 - a)(4^2+4a+a^2)}$

$\mathbf{64 - a^3 =(4 - a)(16+4a+a^2)}$

Hence, the expanded form of $\mathbf{(a)\ 64 - a^3}$ is:

$\mathbf{64 - a^3 =(4 - a)(16+4a+a^2)}$

$\mathbf{(b)\ 75 - n^3}$

Rewrite as:

$\mathbf{75 - n^3 = 5^3 - n^3}$

Expand using: $\mathbf{x^3 -y^3=(x - y)(x^2+xy+y^2)}$

$\mathbf{75 - n^3 = (5- n)(5^2 + 5n + n^2)}$

$\mathbf{75 - n^3 = (5- n)(25 + 5n + n^2)}$

Read more about sums and differences of cubes at:

brainly.com/question/17077929