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Alexeev081 [22]
3 years ago
15

For binomials of the form (x - y) ^ n explain how to determine the sign of a term without writing out the entire expansion

Mathematics
1 answer:
Mnenie [13.5K]3 years ago
3 0

Answer:

When raising an expression of that format to any power, after grouping like terms, you'll always find that the odd numbered terms are positive, and the even numbered terms are negative.

For example:

(x - y)² = x² − 2xy + y²

(x - y)³ = x³ − 3x²y + 3xy² − y³

(x - y)⁴ =x⁴ − 4x³y + 6x²y² − 4xy³ + y⁴

etc.

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The sum of two consecutive odd numbers is 284. Find each number please.
Vlad [161]
We can solve this by finding one of the numbers first
Let the smaller number be y. 
Since these 2 numbers are consecutive odd numbers, the larger number should be 2 more than the smaller one (y+2).

Therefore, 
y + (y+2) = 284
2y +2 = 284
shift +2 to the other side and turn it into -2
2y = 284 - 2
2y = 282
shift x2 to the other side and turn it into /2
y = 282/2
y = 141

Now we got the smaller number, which is 141, we can also find the larger number by adding 2 to it. 141+2 = 143, 
Therefore, your answer is 141 and 143

8 0
3 years ago
Read 2 more answers
Im kinda confused ;-;​
Ivan

Answer:

42-38

42 + (-38)

-38+42

Step-by-step explanation:

In all of these expressions, the 38 has to be negative because that is what you're taking away from the 48. When you have -(- it turns into a +.

In -42 + 38 the 42 is negative, but that is Emma's total amount so it's positive

With -42 -(-38) they did the just added those two together which would make the 42 still negative and the 38 positive.

THen with 42 + 38 the 38 is being subtracted from what she has so you would not add 38 to her total.

7 0
3 years ago
Read 2 more answers
In Exercises 3 and 4, find the values of x and y <br> plz help!!!
jonny [76]

Answer:

x = 20°

y = 30

Step-by-step explanation:

The triangle given on close inspection, it is an equilateral triangle.

Each angle in an equilateral triangle is equal. Likewise, each side is equal.

Thus;

16 + y = 46

y = 46 - 16

y = 30

The triangle that has angle 80°, the other complete angle is 60° because it's an angle of an equilateral triangle.

Thus, the smaller angle there is;

180 - (80 + 60) = 40°

Because sum of angles in a triangle is 180°

Now, x + 40 = 60°

Since that's also an angle of an equilateral triangle.

x = 60 - 40

x = 20°

8 0
3 years ago
What is the volume of the cone below?
Elden [556K]

Answer:

V = 3408 pi  unit^3

Step-by-step explanation:

Volume  of a cone is given by

V = 1/3 pi r^2 h

We know the radius is 12 and the height is 71

V = 1/3 * pi * (12)^2 *71

V = 1/3 * pi * 144 *71

V = 3408 pi  unit^3

7 0
3 years ago
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If Hannah was having 29 apples, and anton takes 9 apples from Hannah,how many apples do Hannah have?
sweet [91]

Answer:

C.

Step-by-step explanation:

It is C. because 29 - 9 equals 20

5 0
3 years ago
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