Answer:
400 is the co-efficient of x⁴
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