Question

Enter the coefficients in the boxes to correctly complete the expanded form of (4x+2y)4 .

__(1)___x4+__(2)____x3y+__(3)___x2y2+__(4)___xy3+___(5)___y4

Answers_ These are right, trust me

(1)_256

(2)_512

(3)_384

(4)_128

(5)_16

Answer 1

1. 256

2. 512

3. 384

4. 128

5. 16

(Buddy here said it--)

Explanation:

Just to make this a little more, uh- Less pointless, here's a joke.

you dont need a parachute to skydive. You need a parachute to skydive twice.

Answer 2

256, 512, 384, 128, 16

Explanation:

You want the coefficients in the expansion of the fourth power of the binomial (4x+2y).

Pascal's triangle

The fourth row of Pascal's triangle gives the coefficients for each product of terms. That row is 1, 4, 6, 4, 1. It tells you ...

(a +b)^4 = 1·a^4b^0 +4·a^3b^1 +6·a^2b^2 +4·a^1b^3 +1·a^0b^4

Application

In the given binomial, we have a=4x, b=2y. Then the expansion is ...

`(4x+2y)^4=(4x)^4+4(4x)^3(2y)+6(4x)^2(2y)^2+4(4x)(2y)^3+(2y)^4\\\\=256x^4+512x^3y+384x^2y^2+128xy^3+16y^4`

The coefficients in order are ...

256, 512, 384, 128, 16

__

Additional comment

The rows of Pascal's triangle are numbered starting from 0.