multiply (5√3 − √2)(5√3 + √2)
Using the formula for the difference of squares, (a - b)(a + b) = a^2 - b^2, we can rewrite the expression as:
(5√3)^2 - (√2)^2
This simplifies to:
25 * 3 - 2
Evaluating the expression, we get:
75 - 2 = 73
Therefore, (5√3 − √2)(5√3 + √2) = 73.
To multiply the expression (5√3 − √2)(5√3 + √2), we can use the FOIL method, which stands for First, Outer, Inner, Last.
First, multiply the first terms:
(5√3)(5√3) = 25(√3)(√3) = 25(3) = 75
Outer, multiply the outer terms:
(5√3)(√2) = 5(√3)(√2) = 5(√6)
Inner, multiply the inner terms:
(−√2)(5√3) = −5(√2)(√3) = −5(√6)
Last, multiply the last terms:
(−√2)(√2) = −(√2)(√2) = −(2) = −2
Now, add all the results together:
75 + 5(√6) - 5(√6) - 2 = 75 - 2
The final simplified answer is:
73
To multiply the given expression (5√3 − √2)(5√3 + √2), we can use the distributive property of multiplication over addition.
Let's break it down step by step:
Step 1: Multiply the first terms
(5√3) * (5√3) = 25 * (√3 * √3) = 25 * 3 = 75
Step 2: Multiply the outer terms
(5√3) * (√2) = 5 * (√3 * √2) = 5 * √(3 * 2) = 5 * √6
Step 3: Multiply the inner terms
(-√2) * (5√3) = -5 * (√2 * √3) = -5 * √(2 * 3) = -5 * √6
Step 4: Multiply the last terms
(-√2) * (√2) = -√(2 * 2) = -√4 = -2
Now, let's combine these results:
Step 5: Add all the results together
75 + 5√6 - 5√6 - 2
Notice that the middle terms (-5√6 and +5√6) cancel each other out because they have opposite signs.
Therefore, the final result is:
75 - 2 = 73
So, (5√3 − √2)(5√3 + √2) simplifies to 73.