Question

(√7-3)²-(√7-1)(√7-5)​

Answer 1

Let's simplify the expression step by step:

1. Start with the given expression: (√7 - 3)² - (√7 - 1)(√7 - 5)

2. Expand the squared term: (√7 - 3)² = (√7 - 3)(√7 - 3) = 7 - 6√7 + 9

3. Expand the product of the two binomials using the FOIL method (First, Outer, Inner, Last): (√7 - 1)(√7 - 5) = (√7 * √7) - 5√7 - √7 + 5 = 7 - 6√7

4. Substitute the expanded expressions back into the original expression: (7 - 6√7 + 9) - (7 - 6√7)

5. Combine like terms: 7 - 6√7 + 9 - 7 + 6√7

6. The terms with √7 cancel out: 7 - 7 + 9

7. Simplify the constants: 0 + 9

8. The final simplified expression is 9.