What is the coefficient of xy^4 in the expansion of (2x+y)^5

The coefficient of xy^4 is 10

Step-by-step explanation:

to solve the questions we proceed as follows:

(2x+y)^5

=(2x+y)²(2x+y)²(2x+y)

We will solve the brackets by whole square formula:

=(4x²+4xy+y²)(4x²+4xy+y²)(2x+y)

By multiplying the brackets we get:

=32x^5+32x^4y+8x³y²+32x^4y+32x³y²+8x²y³+8x³y²+4x²y³+2xy^4+16x^4y+

16x³y²+4x²y³+16x³y²+16x²y³+4xy^4+4x²y³+4xy^4+y^5

=32x^5+80x^4y+80x³y²+40x²y³+10xy^4+y^5

Therefore the coefficient of xy^4 is 10

The answer is 10

correct answer:

i^31 = -i

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.