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

1 Answer
Alexi De Avila Cadena
Dec 6, 2017

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.

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