Question

I had to take some pictures for the two-part question so that is not the answer

Answer 1

- You have the first multiplication problem shown on the left side:

`4x(4x^2-x+3)`

Applying the Distributive property, you get:

`=(4x)(4x^2)+(4x)(-x)+(4x)(3)=16x^3-4x^2+12x`

- The second one is:

`\mleft(8x+1\mright)\mleft(2x-3\mright)`

Solving the multiplication using the FOIL method, you get:

`=(8x)(2x)+(8x)(-3)+(1)(2x)+(1)(-3)=16x^2-24x+2x-3`

Adding the like terms, you get that its simplified form is:

`=16x^2-22x-3`

- The third multiplication problem is:

`4x^2\mleft(4x\mright)`

Solving it, you get:

`=16x^3`

- The fourth one is:

`\mleft(2x+3\mright)\mleft(8x^2-4x+3\mright)`

Multiplying the polynomials, you get:

`\begin{gathered} =(2x)(8x^2)+(2x)(-4x)+(2x)(3)+(3)(8x^2)+(3)(-4x)+(3)(3) \\ =16x^3-8x^2+6x+24x^2-12x+9 \end{gathered}`

Add the like terms:

`=16x^3+16x^2-6x+9`

Therefore, the answer is: