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