I really need help!!!

What is the binomial expansion of (x + 2y)7?

borishaifa [10]

<h2>Thus, the required "option 4)" is correct.</h2>

Step-by-step explanation:

We find,

$(x+2y)^7$

To find, the binomial expansion of of $(x+2y)^7$ = ?

We know that,

$(x+y)^{n} =^nC_0x^n+^nC_1x^{n-1}y+nC_2x^{n-2}y^2+nC_3x^{n-3}y^3+...+^nC_ny^n$

∴ $(x+2y)^7$

Here, n = 7, x = x and y = 2y

$(x+2y)^7$ = $^7C_0x^7+^7C_1x^{7-1}(2y)+^7C_2x^{7-2}(2y)^2+^7C_3x^{7-3}(2y)^3+^7C_4x^{7-4}(2y)^4+^7C_5x^{7-5}(2y)^5+^7C_6x(2y)^6+(2y)^7$ $=x^7+7x^{6(2y)+21x^{5}4y^2+35x^{4}8y^3+^35x^{3}16y^4+21x^{2}32y^5+7x64y^6+128y^7$

$=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7$

∴ The binomial expansion of of $(x+2y)^7$

$=x^7+14x^{6}y+84x^{5}y^2+280x^{4}y^3+560x^{3}y^4+672x^{2}y^5+448xy^6+128y^7$

Thus, the required "option 4)" is correct.

7 0

3 years ago

Triangle ABC has a perimeter of 30in and an area of 30in?. It is dilated by a factor of 2.5 to create triangle A'B'C' What state

chubhunter [2.5K]

Step-by-step explanation:

A triangle has an area of 30cm². The base and height are scaled by a factor of 3. What is the area of the resulting triangle? _cm²

7 0

3 years ago

What is the simplest form of this expression w^2(-4w^2-2)+(-5w^2)(-2w^2-2)

VikaD [51]

Answer:
6w⁴ + 8w²

Explanation:
Before we begin, remember the following:
xᵃ * xᵇ = x⁺ᵇ
+ve * -ve = -ve
-ve * -ve = +ve
+ve * +ve = +ve

To solve this problem, we will follow the following steps:
1- get rid of the brackets using the distributive property
2- combine like terms

This can be shown as follows:
w²(-4w² - 2) + (-5w²)(-2w² - 2)
w²(-4w²) + w²(-2) + (-5w²)(-2w²) + (-5w²)(-2)
-4w⁴ - 2w² + 10w⁴ + 10w²
w⁴(-4+10) + w²(-2+10)
6w⁴ + 8w²

Hope this helps :)

7 0

3 years ago

Read 2 more answers

What is the solution-3x+10=-20

pogonyaev

Answer:

$- 3x + 10 = - 20 \\ - 3x = - 20 - 10 \\ - 3x = - 30 \\ \frac{ - 3x}{ - 3} = \frac{ - 30}{ - 3} \\ x = 10$