Explanation:
(a) To factorize 25t² - 4, we can use the difference of squares formula:
a² - b² = (a + b)(a - b)
In this case, a = 5t and b = 2. So we have:
25t² - 4 = (5t + 2)(5t - 2)
Therefore, 25t² - 4 can be factorized as (5t + 2)(5t - 2).
(b) To factorize x² - 6x - 3xy + 18y, we can group the terms:
(x² - 3xy) - (6x - 18y)
We can then factor out the common factors from each group:
x(x - 3y) - 6(x - 3y)
Notice that both terms have a factor of (x - 3y), so we can factor it out:
(x - 3y)(x - 6)
Therefore, x² - 6x - 3xy + 18y can be factorized as (x - 3y)(x - 6).