What is the coefficient of x2 y4 in 5x 2y6SolutionCoefficie

What is the coefficient of x^2 y^4 in (5x – 2y)^6

Solution

Coefficient is a number used to multiply a variable.

(5x – 2y)^6

= (5x – 2y)^2 *(5x – 2y)^2 *(5x – 2y)^2

= (25x^2 + 4y^2 - 20xy) (25x^2 + 4y^2 - 20xy) (25x^2 + 4y^2 - 20xy)

=(625x^4 + 100x^2y^2 - 500x^3y + 100x^2y^2 + 16y^4 - 80xy^3 - 500x^3y - 80xy^3 + 400x^2y^2)(25x^2 + 4y^2 - 20xy)

=(625x^4 + 600x^2y^2 -1000x^3y + 16y^4 -160xy^3)(25x^2 + 4y^2 - 20xy)

= (15625x^6 + 2500x^4y^2 -1250x^5y + 15000x^4y^2 + 2400x^2y^4 - 12000x^3y^3 - 25000x^5y - 4000x^3y^3 + 20000x^4y^2 + 400x^2y^4 + 64y^6 - 320xy^5 - 4000x^3y^3 - 640xy^5 + 3200x^2y^4)

= 15625x^6 + 37500x^4y^2 - 26250x^5y + 6000x^2y^4 - 20000x^3y^3 + 64y^6 - 960xy^5

So the coefficient of x^2 y^4 in (5x – 2y)^6 is 6000.