If this is for factoring, here’s how to do it.
7. 45n^2-5
-first, ask yourself what common factor does 45n^2 and 5 have? The answer is that they’re both divisible by 5
-next you want to expand this expression by dividing 5 out and rewriting it in multiplication. If you completely remove the 5 from the expression, you have created a new and different expression (which is not the goal). And so you will have: 5(9n^2-1)
-now we have to expand 9n^2-1. We know that (a-b)(a+b)=a^2-b^2; once you foil and multiply the expression, you’ll notice you cancelled ab with ab. So for this problem, you need to see what will make 9 and 1 once you square them(It’s 3 and 1).
-what you should have now is 5(3n-1)(3n+1). But ways check by foiling your answer to see if you end up with the same expression.
9. 45a^3-80a
what is similar about 45a^3 and 80a?
- both divisible by 5a
5a(9a^2-16)
what do you square to get 9 and 16
- 3 and 4
5a(3a-4)(3a+4)
When it comes to bigger numbers, use the quadratic formula to find the variables that‘ll be part of your factored answers(Remember to apply the opposite sign/operation when you insert the numbers you got from the formula - because the numbers from the formula are the solutions ex. If I got 3 and -4 from the formula, my factored expression would be (X-3)(X+4))