Question

Fully factorise 75x^2-3. The answer is 3(5x+1)(5x-1) . Can someone fully explain how to get that???

Answer 1

first note that the greatest common factor of 75 and 3 is 3
so you can take 3 out to give
3(25x^2 - 1)

now in the parentheses we have the difference of 2 squares 25x^2 and 1 aer both perfect squares so we can apply the identity

a^2 - b^2 = (a + b)(a - b)

letting a = square root of 25x^2 ( that is 5x ) and b^2 = 1 ( therefore b = 1), we get

3(5x + 1)(5x - 1)

Answer 2

ok?

Answer 3

Thanks I think i sort of get it now