What is the coefficient of x2y3 in the expansion of (2x + y)5?
ОА. 2
Ов. 5
Ос. 40
OD.
E. It does not exist.

Option C:

The coefficient of is 40.

Solution:

Given expression:

Using binomial theorem:

Here

Substitute in the binomial formula, we get

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

Let us solve the term one by one.

Substitute these into the above expansion.

The coefficient of is 40.

Option C is the correct answer.

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step-by-step explanation:

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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