Question

Expand (2x² + y³)⁵using combinations.

Answer 1

$$(2x^2 + y^3)^5=\dbinom{5}{0}(2x^2)^5(y^3)^0$$

$$+\dbinom{5}{1}(2x^2)^4(y^3)^1+\dbinom{5}{2}(2x^2)^3(y^3)^2$$

$$+\dbinom{5}{3}(2x^2)^2(y^3)^3+\dbinom{5}{4}(2x^2)^1(y^3)^4$$

$$+\dbinom{5}{5}(2x^2)^0(y^3)^5$$

$$=32x^{10}+80x^8y^3+80x^6y^6+40x^4y^9$$

$$+10x^2y^{12}+y^{15}$$