Final answer:
To factorize the given expressions, we can use the quadratic formula for the first expression and the difference of squares identity for the second expression.
Step-by-step explanation:
To factorize the given expressions:
(i) 4x² - 4y + 1
By looking at the expression, we can see that it cannot be easily factored using identities. We can, however, use the quadratic formula to find the roots of the quadratic equation and express the expression as a product of linear factors. Using the formula, the roots of the equation are:
x = ±√(1 - y)
Therefore, the factored form is:
4x² - 4y + 1 = 4(x - √(1 - y))(x + √(1 - y))
(ii) x² - y²/100
Using the difference of squares identity, the expression can be factored as:
x² - y²/100 = (x - y/10)(x + y/10)