Chapter 8.3, Problem 57PFA

a.

To determine

To find: The product $\left(2x-3\right)\left(x^2-4x+1\right)$

Answer to Problem 57PFA

  $2x^3-11x^2+14x-3$

Explanation of Solution

Given:

  $\left(2x-3\right)\left(x^2-4x+1\right)$

Calculation:

It has been given that $\left(2x-3\right)\left(x^2-4x+1\right)$

In order to multiply, apply the distributive property

  $2x\cdot x^2+2x\cdot \left(-4x\right)+2x\cdot 1-3\cdot x^2-3\cdot \left(-4x\right)-3\cdot 1$

Simplify this expression

  $2x^3-8x^2+2x-3x^2+12x-3$

Combine the like terms

  $2x^3-11x^2+14x-3$

b.

To determine

To find: The product $\left(3x-3\right)\left(2x^2-4x+1\right)$

Answer to Problem 57PFA

  $2x^3-15x^2+15x-3$

Explanation of Solution

Given:

  $\left(3x-3\right)\left(2x^2-4x+1\right)$

Calculation:

It has been given that $\left(3x-3\right)\left(2x^2-4x+1\right)$

In order to multiply, apply the distributive property

  $2x\cdot x^2+3x\cdot \left(-4x\right)+3x\cdot 1-3\cdot x^2-3\cdot \left(-4x\right)-3\cdot 1$

Simplify this expression

  $2x^3-12x^2+3x-3x^2+12x-3$

Combine the like terms

  $2x^3-15x^2+15x-3$