4. Factorize: Factorize: (i) \( x^{2}-12 x- \) Factorize: Find HCF (i) \( (a+b)^{2}, a^{2}-b^{2} \)

Let's tackle each part of your request step by step. ### Part 1: Factorize \( x^{2} - 12x \) To factor the expression \( x^{2} - 12x \), we can look for common factors: 1. Identify the common factor: Both terms have \( x \) as a common factor. 2. Factor out \( x \): \[ x^{2} - 12x = x(x - 12) \] So, the factorization of \( x^{2} - 12x \) is: \[ x(x - 12) \] ### Part 2: Find HCF of \( (a+b)^{2} \) and \( a^{2}-b^{2} \) To find the highest common factor (HCF) of the two expressions \( (a+b)^{2} \) and \( a^{2}-b^{2} \), we can first factor each expression. 1. **Factor \( (a+b)^{2} \)**: - This is already in its factored form. 2. **Factor \( a^{2} - b^{2} \)**: - This is a difference of squares, which can be factored as: \[ a^{2} - b^{2} = (a - b)(a + b) \] Now we have: - \( (a+b)^{2} \) - \( (a-b)(a+b) \) ### Finding the HCF: The common factor in both expressions is \( (a+b) \). Thus, the HCF of \( (a+b)^{2} \) and \( a^{2}-b^{2} \) is: \[ (a+b) \] ### Summary: 1. The factorization of \( x^{2} - 12x \) is \( x(x - 12) \). 2. The HCF of \( (a+b)^{2} \) and \( a^{2}-b^{2} \) is \( (a+b) \).