How to factorise these terms?

Question

2mn+m²-6n-3m

4y²-81

t²-6t+8

Any assistance would be really appreciated.

Answer 1

4y^2 - 81

= (2y)^2 - 9^2 = (2y-9)(2y+9) there's a general formula a^2-b^2 = (a-b)(a+b) the difference of 2 squares = the product of the sum and difference of what was squared.

t^2 -6t + 8 look at the 8 and consider its integer factors, 8,1, or 2 and 4, find a sum of two of them that = 6

2 and 4 sum to +1, so make them negative, -2 and -4 sum to -6

= (t-2)(t-4)