Factorising difference of perfect squares?

In factorising, you must factorise the numbers until it can't be factorised anymore.

In fact your answer 4x^2 - 100 = (2x - 10)(2x + 10) is not correct because (2x - 10) and (2x + 10) can be factorised further....

2x - 10 = 2(x - 5)
2x + 10 = 2(x + 5)

Therefore,
4x^2 - 100 = 2(x - 5)(2)(x + 5)
4x^2 - 100 = 4(x - 5)(x + 5)

a million) (x - a million)^2 = 16 x - a million = +/- Sqrt 16 x = a million +/- 4 x = a million + 4 = 5 x = a million - 4 = - 3 2) (x + 3)^2 - 4x^2 x^2 + 6x + 9 - 4x^2 - 3x^2 + 6x + 9 3x^2 - 6x - 9 3(x^2 - 2x - 3) 3(x - a million)^2 - a million - 3 = 0 3(x - a million)^2 = 4 (x - a million) = +/- Sqrt4 x - a million = +/- 2 x = a million +/- 2) x = a million + 2 = 3 x = a million - 2 = - a million 3) (3x - a million)^2 - (x + a million)^2 9x^2 - 6x + a million - x^2 + 2x + a million 8x^2 - 8x 8x(x - a million) = 0 x = 0, x = a million

Normal procedure is to take out a common factor first of all.

4x² - 100
4 (x² - 25)
4 (x - 5)(x + 5)

4m² - 81 does not have a common factor
(2m - 9)(2m + 9)

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

1)
4x^2 - 100
= (2x)^2 - 10^2
= (2x + 10)(2x - 10)
= 2(x + 5)(2x - 10)
= 2(2)(x + 5)(x - 5)
= 4(x + 5)(x - 5)

2)
4m^2 - 81
= (2m)^2 - 9^2
= (2m + 9)(2m - 9)

You should pull out a common factor, before doing the hard part.

4x^2 - 100

4 (x^2 - 25) This is the key step.

4 (x+5)(x-5)

Your correct, but your answer can be factored further, and sometimes thats what teachers look for.
ur answer has a common factor that can be divided out, and when you have a factoring question, it is assumed u factor completely.

Its 100 % correct

You're correct!!!

4x²-100 = (2x-10)(2x+10)

That is the correct answer!