Question

Which product of factors is equivalent to x100–36?

(x10–6)(x10+6)

(x50–6)(x50+6)

(x50–18)(x50+18)

(x10–18)(x10+18)

Answer 1

`( {x}^(10) )^(2) - {6}^(2) = ({x}^(10) - {6}) ( {x}^(10) + {6})`

Step-by-step explanation

The given expression is:

`{x}^(100) - 36`

We can rewrite this expression as:

`( {x}^(10) )^(2) - {6}^(2)`

We have now written the expression as a difference of two squares:

Recall that:

`{a}^(2) - {b}^(2) = (a - b)(a + b)`

This implies that,

`( {x}^(10) )^(2) - {6}^(2) = ({x}^(10) - {6}) ( {x}^(10) + {6})`