Question

3x^2(x^3-1)+2x^3(2x^2+2)
Whats the simplified answer?

Answer 1

`\large\boxed{7x^5+4x^3-3x^2}`

Explanation:

`3x^2(x^3-1)+2x^3(2x^2+2)\qquad\text{use the distributive property:}\ a(b+c)=ab+ac\\\\=(3x^2)(x^3)+(3x^2)(-1)+(2x^3)(2x^2)+(2x^3)(2)\qquad\text{use}\ a^na^m=a^(n+m)\\\\=3x^(2+3)-3x^2+4x^(3+2)+4x^3\\\\=3x^5-3x^2+4x^5+4x^3\qquad\text{combine like terms}\\\\=(3x^5+4x^5)-3x^2+4x^3\\\\=7x^5+4x^3-3x^2`