Factor 48a^2-75 (show work if you dont mind)?

Answer 1

Common factor is 3:

3 * (16a^2 - 25)

However, both terms (16a^2 and 25) are perfect squares, and the factoring of the difference of two squares (x^2 - y^2) is (x - y)(x + y).

So this further factors to:

3 * (sqrt(16a^2) + sqrt(25))(sqrt(16a^2) - sqrt(25))
3 * (4a + 5) (4a - 5)

Answer 2

48a² - 75
Do 48 and 75 have a common factor?
Try 3
3(16)a² - 3(25)
Because of a thing called distributivity that says a(b+c) = ab+ac
3(16)a² - 3(25) = 3(16a² - 25)

(16a² - 25) looks a lot like the form (a² - b²) that we know factors into (a+b)(a-b)
16a² = (4a)² and 25 = 5²
So 3(a² - 25) factors further into 3(4a + 5)(4a – 5)

Answer 3

The only thing common between the two terms is 3

48a^2 - 75 =

(3*16)a^2 - (3*25) =

3(16a^2 - 25)

oops.....Difference of Squares

3(4a + 5)(4a - 5)

Answer 4

First: find the Greatest Common Factor or, find a term divisible with the expression which, is 3.

3(25a^2-16)

Sec: factor the inner expression which, is the difference of squares.

3(5a*5a - 4*4)

3(5a + 4)(5a - 4)