Question

How do you expand the binomial `(2x-y^2)^7` using the binomial theorem?

Answer 1

`(2x-y^2)^7=128x^7-448x^6 y^2+672x^5 y^4-560x^4 y^6+280x^3 y^8-84x^2 y^10+14x y^12-y^14`

Explanation:

Using Binomial Theorem

`(2x-y^2)^7=(2x)^7+7/(1!)(2x)^6*(-y^2)^1+(7*6)/(2!)(2x)^5*(-y^2)^2+(7*6*5)/(3!)*(2x)^4(-y^2)^3+(7*6*5*4)/(4!)(2x)^3(-y^2)^4+(7*6*5*4*3)/(5!)(2x)^2(-y^2)^5+(7*6*5*4*3*2)/(6!)(2x)^1(-y^2)^6+(7*6*5*4*3*2*1)/(7!)(2x)^0(-y^2)^7`

`(2x-y^2)^7=128x^7-7(64x^6)*(y^2)+(21)(32x^5)(y^4)-(35)(16x^4)(y^6)+(35)(8x^3)(y^8)-(21)(4x^2)(y^10)+(7)(2x)(y^12)-(1)(y^14)`

`(2x-y^2)^7=128x^7-448x^6 y^2+672x^5 y^4-560x^4 y^6+280x^3 y^8-84x^2 y^10+14x y^12-y^14`

God bless....I hope the explanation is useful.