Question

Multiply. Check picture.

Answer 1

The answer is $3x^4-13x^3-x^2-11x+6$.

Solution:

Use algebraic identity: $a^m\times a^n=a^{m+n}$

For example: $x^2\times x=x^{2+1}=x^3$

Given expression $(x^2-5x+2)$ and $(3x^2+2x+3)$.

To multiply these equations.

$(x^2-5x+2)\times(3x^2+2x+3)$

             $=x^2(3x^2+2x+3)-5x(3x^2+2x+3)+2(3x^2+2x+3)$

             $=(3x^4+2x^3+3x^2)+(-15x^3-10x^2-15x)+(6x^2+4x+6)$

             $=3x^4+2x^3+3x^2-15x^3-10x^2-15x+6x^2+4x+6$

Combine like terms together.

             $=3x^4+(2x^3-15x^3)+(3x^2-10x^2+6x^2)-15x+4x+6$

             $=3x^4-13x^3-x^2-11x+6$

$(x^2-5x+2)\times(3x^2+2x+3)=3x^4-13x^3-x^2-11x+6$

Hence the answer is $3x^4-13x^3-x^2-11x+6$.