Find the H. C.F of the following expressions. 1) 16x⁴ - 4x² - 4x - 1 , 8x³ - 1

2) 9x² - 4y² - 8yz - 4z² , 4z² - 4y² - 9x² - 12xy , 9x² + 12xz + 4z² - 4y²

3) x² - 18x - 19 + 20y - y² , x² + x - y² + y , x² - y² + 2y - 1

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Step 1: Write the first expression given in the question.

Step 2: Here, we are finding H.C.F. using factorisation. So, find the factors of the first expression. We find the factors using the formula (a²-b²) = (a+b)(a-b).

Step 3: Write the second expression given in the question.

Step 4: This expression is an expanded form of (a+b)² = (a²+2ab+b²). So, we write it in square form.

Step 5: To make it easy to find HCF, we write (x+y)² in factor form.

Step 6: Write the H.C.F. (Highest Common Factor) of the given expressions by analysing the factors you generated in each expressions. Here, (x+2) are the only common factors.

step-by-step explanation:

a and d