Hi

Just wandering

When I factorise the following :

4s-16t+20r

It will equal to 2 ( 2s - 8t + 10 r )
This was the answer in the book

However , I managed to factorise it to become :

4 ( s-4t+5r)

is this correct ? Because when you multiple it out , it gives you the same anwer which is 4s-16t-20r

Also , another one was :

56x^2y - 28 xy^2

In the book the anwer gave me : 7xy ( 8x - 4y)

I got 28xy ( 2y - y)

Is this the same ?

If not .. why ?

You are correct on both counts, the book is in error.

Hi!

Let's take a look at the factorizations you provided and determine if they are correct.

For the first expression, 4s - 16t + 20r, you factored it as 4(s - 4t + 5r). Let's multiply it out and see if we get the same result as the original expression:

4(s - 4t + 5r) = 4s - 16t + 20r

As you can see, the product does indeed equal the original expression. Therefore, your factorization is correct!

For the second expression, 56x^2y - 28xy^2, you factored it as 28xy(2y - y). Let's multiply it out and compare it to the original expression:

28xy(2y - y) = 56x^2y^2 - 28xy^2

As you can see, the product is not the same as the original expression. The original expression has a term of -28xy^2, but your factorization has a term of -28xy^3. Therefore, your factorization is incorrect.

The correct factorization of 56x^2y - 28xy^2 is 7xy(8x - 4y). Let's multiply it out to confirm:

7xy(8x - 4y) = 56x^2y - 28xy^2

As you can see, the product is indeed the same as the original expression. Therefore, the answer provided in the book is correct.

The reason why your factorization is incorrect is because you mistakenly factored out an extra "y" term. When factoring, you need to ensure that you are factoring out the greatest common factor of all the terms.

I hope this clears up any confusion! Let me know if you have any further questions.