Grade 10 math homework help on factoring

so the "pattern" is (a+b)(a-b) = a^2-b^2

how do I solve
(x-7)(x+5)

Thank you for your help! much appreciated

Have you heard of the FOIL method? It goes multiply the (F)irst then multiply the (O)utside terms, then the (I)nside terms, then finally the (L)ast term. Then you combine them together.

So x*x= x^2, and x*5=5x, x*(-7)=-7x, and (-7)(5)=-35

Then combine:
x^2+5x-7x-35

So the answer is x^2-2x-35

This works with all factoring problems like this and will help you alot as you progress in math. Hope it helps :)

(x - 7) times (x - 5)

x - 7
x - 5
___

x^2 - 7x
-5x + 35
_________

x^2 - 12x + 35

The x intercepts are 7 and -5
If you wanted those multiplied it's x^2-2x-35