Question

How do you factor completely `56a^2b^3 - 35ab`?

Answer 1

See a solution process below:

Explanation:

We can factor each term as:

`56a^2b^3 = 2 xx 2 xx 2 xx 7 xx a xx a xx b xx b xx b`

`35ab = 5 xx 7 xx a xx b`

The common factors are in read:

`56a^2b^3 = 2 xx 2 xx 2 xx color(red)(7) xx color(red)(a) xx a xx color(red)(b) xx b xx b`

`35ab = 5 xx color(red)(7) xx color(red)(a) xx color(red)(b)`

Therefore the common factor is:

`color(red)(7) xx color(red)(a) xx color(red)(b) = color(red)(7ab)`

We can now write the expression as the product of the common factor and the remaining factors for each term:

`color(red)(7ab)([2 xx 2 xx 2 xx a xx b xx b] - 5) =>`

`color(red)(7ab)(8ab^2 - 5)`