factor 50x^2-72
50 x ^ 2 - 72 =
2 ( 25 x ^ 2 - 36 )=
2 [ ( 5 x ) ^2 - ( 6 ) ^2 ] =
2 ( 5x - 6 ) ( 5x + 6 )
To factor the expression 50x^2 - 72, we can start by looking for common factors. In this case, we can divide the expression by 2 since both terms are divisible by 2:
(50x^2 - 72) ÷ 2 = 25x^2 - 36
Now, let's try to factor the remaining quadratic expression, 25x^2 - 36. It helps to recognize that this is a difference of squares, since 25x^2 is the square of 5x, and 36 is the square of 6:
25x^2 - 36 = (5x)^2 - 6^2
Now, we can use the formula for factoring a difference of squares, which states that a^2 - b^2 = (a + b)(a - b).
Using this formula, we can rewrite the expression as a product:
(5x + 6)(5x - 6)
Therefore, the factored form of 50x^2 - 72 is (5x + 6)(5x - 6).