multiply(square root5 +1)(8 square root5 +1)
I will be happy to critique your work. Use FOIL>
....
= 40 + √5 + 8√5 + 1
= 41 + 9√5
To multiply the expressions (√5 + 1) and (8√5 + 1), you can use the distributive property of multiplication over addition.
The distributive property states that for any numbers a, b, and c, the product of a and the sum of b and c is equal to the sum of the products of a and b and a and c.
In this case, you can treat (√5 + 1) as a single term and multiply it by each term in (8√5 + 1).
Let's break down the multiplication step by step:
Step 1: Multiply the first terms.
First term of (√5 + 1) x first term of (8√5 + 1):
(√5)(8√5) = 8(√5)^2 = 8(√5 * √5) = 8(√(5*5)) = 8(√25) = 8(5) = 40
Step 2: Multiply the outer terms.
First term of (√5 + 1) x second term of (8√5 + 1):
(√5)(1) = √5
Step 3: Multiply the inner terms.
Second term of (√5 + 1) x first term of (8√5 + 1):
(1)(8√5) = 8√5
Step 4: Multiply the last terms.
Second term of (√5 + 1) x second term of (8√5 + 1):
(1)(1) = 1
Step 5: Combine the like terms obtained from the above steps.
40 + √5 + 8√5 + 1 = 41 + 9√5
Therefore, the product of (√5 + 1) and (8√5 + 1) is 41 + 9√5.