All categories

3 years ago

Binomial theorem Expand (5 - y)3

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

7 0

Answer:

(5 - y) ^3 = 125 - 75y + 15y^2 - y^3

Step-by-step explanation:

Binomial expression

1. 1

1. 2. 1

1. 3. 3. 1 --------power of 3

( 5 - y) ^3

( 5 - y) (5 - y) (5 - y)

( a + b) ^3 = a^3 + 3a^2b + 3ab^2 + b^3

a = 5

b = -y

( 5 - y) ^2 = ( 5 - y) (5 - y)

= 5( 5 - y) - y(5 - y)

= 25 - 5y - 5y + y^2

=(25-10y+y^2)

( 25 - 10y + y^2)( 5 - y)

= 5(25 - 10y + y^2) - y( 25 - 10y + y^2)

= 125 - 50y + 5y^2 - 25y + 10y^2 - y^3

Collect the like terms

= 125 - 50y - 25y + 5y^2 + 10y^2 - y^3

= 125 - 75y + 15y^2 - y^3

You might be interested in

Can y’all help me me on question 2?! Have a good day!

AfilCa [17]

Answer:

Step-by-step explanation:

The formula to get the area of a triangle is A= $\frac{(b)(h)}{2}$ so all you have to do is work backwards. 18x2=36. 36/4=9.

6 0

3 years ago

What is the equation of the graphed linear model? y = x +

timofeeve [1]

Answer:

y = - 2x + 110

Step-by-step explanation:

The equation of a line in slope- intercept form is

y + mx + c ( m is the slope and c the y- intercept )

To calculate m use the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 110) and (x₂, y₂ ) = (20, 70) ← 2 points on the line

m = $\frac{70-110}{20-0}$ = $\frac{-40}{20}$ = - 2

the line crosses the y- axis at (0, 110) ⇒ c = 110

y = - 2x + 110 ← equation of line

7 0

3 years ago

Find the missing factor 2x^2+15x+7=(2x+1)(?)

Genrish500 [490]

Answer:

? = (x + 7)

Step-by-step explanation:

2x^2 + 15x + 7 = (2x + 1) (?)

1. First you need to figure out what multiplied by 2x will give you 2x^2, which is x.

2. Then you need to find what would give you 15x. In this case because you have the 1 in (2x + 1), you already know that there is going to be an extra x. So, what times 2x gives you 14x? It's 7.

3. Lastly you need to make sure that 1 multiplied with 7 is equal to 7 and combine like terms.

4. Check: (2x + 1) (x + 7) =

2x^2 + 14x + 1x + 7 =

2x^2 + 15x + 7

5 0

3 years ago

Why does 20x700=14000 please give details

Butoxors [25]

Answer:

When multiplying zeros, you first remove the zeros.

So,

2 x 7 = 14

Then you add the zeros to the answer.

We had three zeros

So we add three zeros to 14

14,000

8 0

3 years ago

Given the Arithmetic sequence A1,A2,A3,A4A1,A2,A3,A4

Bad White [126]

The given sequence is
a₁ = 29
a₂ = 39
a₃ = 49
a₄ = 59

This sequence is an arithmetic sequence. Th first term is a₁ = 29, and the common difference is d= 10.

The n-th term is
$a_{n}=a_{1}+(n-1)d$
The 33-rd termis
a₃₃ = 29 + (33 - 1)*10
= 29 + 320
= 349

Answer: a₃₃ = 349

7 0

3 years ago