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Mazyrski [523]
3 years ago
10

Find the product. (–7t – 5v)(–4t – 3v)

Mathematics
1 answer:
Anuta_ua [19.1K]3 years ago
7 0

Answer: Option B is the correct answer

Step-by-step explanation:

The given expression is

(–7t – 5v)(–4t – 3v).

The product will be a quadratic equation (having 2 as the highest power)

To find the product, we would expand the brackets

(-7t × -4t )+ (-7t × -3v) + (-5v × -4t) + (-5v × - 3v)

= (- -28t^2) +(- -21tv) + (- - 20tv) +(- -15v^2)

Recall, negative × negative equals positive.

=28t^2 +21tv +20tv+ 15v^2)

Collecting like terms, we add all terms containing the same letters together

28t^2 + 41tv + 15v^2

Option B is the correct answer

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3 years ago
N is a positive integer
Murrr4er [49]

Part (1)

n is some positive integer. Let's say for now that n is even. So n = 2k, for some integer k

This means n-1 = 2k-1 is odd since subtracting 1 from an even number leads to an odd number.

Now multiply n with n-1 to get

n(n-1) = 2k(2k-1) = 2m

where m = k(2k-1) is an integer

The result 2m is even showing that n(n-1) is even

------------

Let's say that n is odd this time. That means n = 2k+1 for some integer k

And also n-1 = 2k+1-1 = 2k showing n-1 is even

Now multiply n and n-1

n(n-1) = (2k+1)(2k) = 2k(2k+1) = 2m

where m = k(2k+1) is an integer

We've shown that n(n-1) is even here as well.

------------

So overall, n(n-1) is even regardless if n is even or if n is odd.

Either n or n-1 will be even. If you multiply an even number with any number, the result will be even.

=======================================================

Part (2)

n is some positive integer

2n is always even since 2 is a factor of 2n

2n+1 is always odd because we're adding 1 to an even number. The sequence of integers goes even,odd,even,odd, etc and it does this forever.

-----------

Another way to see how 2n+1 is odd is to divide 2n+1 over 2 and you'll find that we get (2n+1)/2 = 2n/2+1/2 = n+0.5

The 0.5 at the end is not an integer, so there's no way that (2n+1)/2 is an integer; therefore 2n+1 is odd.

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