Question

Find the HCF of a²-(b+c)²andb²-(c+a)² and second question y²+4y+4andy²+6y+8 step by step

Answer 1

To find the HCF of the given expressions, we can factorize each expression and identify the common factor. For the first question, the HCF is a² - b² - 2bc - c². For the second question, the HCF is y+2.

Step-by-step explanation:

The first question is asking you to find the Highest Common Factor (HCF) of the expressions a²-(b+c)² and b²-(c+a)². To find the HCF, we need to factorize each expression and identify the common factors. Let's solve it step by step:

1. Factorize the first expression:
   a²-(b+c)² = a² - (b+c)(b+c) = a² - (b² + 2bc + c²) = a² - b² - 2bc - c²
2. Factorize the second expression:
   b²-(c+a)² = b² - (c+a)(c+a) = b² - (c² + 2ac + a²) = b² - c² - 2ac - a²
3. Now, we can see that both expressions have common factors: a² - b² and -2bc - 2ac - c² - a²
4. Thus, the HCF of the two expressions is a² - b² - 2bc - c²

For the second question regarding the expression y²+4y+4 and y²+6y+8, we can use the same approach to find the HCF:

1. Factorize the first expression:
   y²+4y+4 = (y+2)(y+2) = (y+2)²
2. Factorize the second expression:
   y²+6y+8 = (y+2)(y+4)
3. The common factor is y+2

Therefore, the HCF of the two expressions is y+2.