Question

How do you factor `5a ^ { 2} - 24a b - 5b ^ { 2}`?

Answer 1

Approach like a normal factoring problem. ( I used Guess and Check.)

Explanation:

If `x^2-y-z`

Then to factor, consider the following `(a+b)(c-d)`
Where `x^2` equals to `a*c`
`y` equals to `(a*c)+(b*d)`
`z` equals to `(b*d)`
And each is a variable representing any number (they are just placeholders.)

Consider it as `5a^2-24a-5`
To get 25, you multiply 5 and 5.
And since 25-1 = 24, and we already have a 5 in front of `a`.
And to get a negative c value and negative b value, we need the larger number to be negative. We could use 5 and 5 but remembering we need one in front of `a` so the other 5 goes to this `c` value

# (5a+b)(a-5b)#
To check, use the distributive property
#5a^2-25ab+ab-5b^2; 5a^2-24ab-5b^2#
Really, the b values may seem difficult but they follow the same principle.