Hence find the coefficient of x^4 in the expansion of (1+x^2)^2(2+x^2)^5

Answer 1

(1+x^2)^2(2+x^2)^5 what is the coefficient of the x^4 term after expanding the factors?

=(1+2x^2 +x^4)(2^5 + 5(2^4)(x^2) + 5!/3!2!(2^3)(x^4) +....+ x^10)

2^5(x^4) + 2x^2(5)(2^4)(x^2) + 10(2^3)(x^4)

= 32x^4 + 160x^4 + 80x^4

= 272x^4

the coefficient is 272