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

step-by-step explanation:

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)