Question

25. Explain the Error Jeremy factored 144x? – 100 as follows:

144x2 100 = (12x + 10)(12x – 10)
= 2(6x + 5)(6x – 5)
What was his error? Correct his work.

Answer 1

Given:

Consider the expression is

`144x^2-100`

Jeremy factored the given expression and his steps are given.

To find:

The error in his solution.

Solution:

We have,

`144x^2-100`

It can be written as

`=12^2x^2-10^2`

`=(12x)^2-10^2`

`=(12x+10)(12x-10)`
`[\because a^2-b^2=(a+b)(a-b)]`

Taking out common factors from each parenthesis.

`=2(6x+5)2(6x-5)`

`=4(6x+5)(6x-5)`

So, Jeremy was incorrect because the common factor is
`2* 2=4` instead of 2.

Therefore, Jeremy made his mistake in his last step.