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

400 is the co-efficient of x⁴

Step-by-step explanation:

(2x +y)⁵= (2x+5)²(2x+5)³= (2x+5) (2x+5)⁴  (breaking the exponents)

= (2x+5) ( 2x+5)²(2x+5)²  (applying the square formula)

=(2x+5) {( 2x)² +2(2x) (5) + (5)²} {( 2x)² +2(2x) (5) + (5)²}

= (2x+5) {(4x²+ 20x+25)}{(4x²+ 20x+25)}  (multiplying the two square formulas to get exponent of 4

= (2x+5) { 16x⁴+ 80x³+100x²+ 80x³+ 400x²+ 500x+ 100x²+500x + 625)}

Summing up  the equation

= (2x+5) { 16x⁴+160x³+600x²+1000x+ 625 }

Multiplying

= 32x⁵+ 320x⁴+ 1200x³+2000x²+1250x+ 80x⁴+800x³+ 3000x² + 5000x+ 3125

Again Summing

= 32x⁵ +400x⁴+ 2000x³+5000x²+6250x +3125

the central idea is that:

individuals should refuse to cooperate with institutions they believe unjust.

thoreau felt  that governments were more often agents of corruption than justice, even democracies, and that just because the majority feels a certain way does not make it just or correct in absolute terms. he uses the fact that slavery exists in our democracy to support this idea.

he goes on to say that, as a result, people should live true to their own internal laws regarding right and wrong, as a product of reflection and a moral life, rather than following every law that society imposes. 

step-by-step explanation: