Answer:
To multiply and simplify the expression (3 - √5)(7 - √5), we can use the distributive property of multiplication.
Step 1: Multiply the first terms of each binomial:
(3 - √5)(7 - √5) = 3 * 7
Step 2: Multiply the outer terms of each binomial:
(3 - √5)(7 - √5) = 3 * (-√5)
Step 3: Multiply the inner terms of each binomial:
(3 - √5)(7 - √5) = (-√5) * 7
Step 4: Multiply the last terms of each binomial:
(3 - √5)(7 - √5) = (-√5) * (-√5)
Now, let's simplify each multiplication:
Step 1: Multiply the first terms: 3 * 7 = 21
Step 2: Multiply the outer terms: 3 * (-√5) = -3√5
Step 3: Multiply the inner terms: (-√5) * 7 = -7√5
Step 4: Multiply the last terms: (-√5) * (-√5) = 5
Finally, let's add the simplified multiplications together:
21 + (-3√5) + (-7√5) + 5
Combining like terms, we have:
21 + 5 + (-3√5) + (-7√5) = 26 - 10√5
Therefore, the simplified form of (3 - √5)(7 - √5) is 26 - 10√5.
Explanation: