Question

Simplify the expression to a polynomial in standard form: (3x + 2)(-3x2 - 7x + 3)

Answer 1

The distributive property for multiplication is given by,

`a(b+c+d)=ab+ac+ad`

Using the above property, the given polynomial can be simplified as,

`\begin{gathered} (3x+2)(-3x^2-7x+3) \\ =3x(-3x^2-7x+3)+2(-3x^2-7x+3) \\ =3x*(-3x^2)+3x*(-7x)+3x*3+2*(-3x^2)+2*(-7x)+2*3 \\ =-9x^2-21x+9x-6x^2-14x+6 \end{gathered}`

Now, comine the like terms and arrange the terms in the desceding order in which the exponents of variables comes.

`\begin{gathered} (-9x^2-6x^2)-21x-14x+6 \\ =-15x^2-35x+6 \\ \text{Therefore, the standard simplified form of the polynomial is} \\ -15x^2-35x+6 \end{gathered}`