Multiply (7–√) (−2–√) . Give an exact answer.
We can use the FOIL method to multiply the binomials:
(7 - √5)(-2 - √5) = 7(-2) + 7(-√5) - √5(-2) - √5(-√5)
Simplifying each term:
= -14 - 7√5 + 2√5 + 5
Combining like terms:
= -14 - 5 - 7√5 + 2√5
= -19 - 5√5
So, (7 - √5)(-2 - √5) = -19 - 5√5.
To multiply (7–√(-1))(-2–√(-1)), we can use the FOIL method.
FOIL stands for First, Outer, Inner, Last.
First: Multiply the first terms in each binomial together.
(7)(-2) = -14
Outer: Multiply the outer terms in each binomial together.
(7)(-√(-1)) = -7√(-1)
Inner: Multiply the inner terms in each binomial together.
(-√(-1))(-2) = 2√(-1)
Last: Multiply the last terms in each binomial together.
(-√(-1))(√(-1)) = -(-1) = 1
Now, let's add all of these terms together to find the product:
-14 + (-7√(-1)) + (2√(-1)) + 1
Simplifying:
-14 - 7√(-1) + 2√(-1) + 1
-14 - 5√(-1) + 1
-13 - 5√(-1)
So, the exact answer is -13 - 5√(-1).
To multiply (7–√) and (−2–√), we can use the distributive property of multiplication over addition.
First, let's multiply the two binomials:
(7–√) * (−2–√)
Using the distributive property:
= 7 * (−2) + 7 * (−√) + (−√) * (−2) + (−√) * (−√)
Simplifying:
= −14 − 7√ − 2√ + √²
Since √² is equal to the square of the square root, we can simplify:
= −14 − 7√ − 2√ + (√² = √)
Now, combining like terms:
= −14 − 9√ + √
Since √ is equal to 1√, we can simplify further:
= −14 − 8√
Therefore, the exact answer of multiplying (7–√) and (−2–√) is −14 − 8√.