Question

Enter your answer and show all the steps that you use to solve this problem in the space provided.

Multiply and simplify if possible.

(3−√5) (7−√5)

Answer 1

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: