Chapter 4.6, Problem 34WE

To determine

To multiply: the given expression

Answer to Problem 34WE

Multiplying the expression given we end up getting $\boxed{-2a^3-5a^2+11a-4}$

Explanation of Solution

Given information: $\left(1-2a\right)\left(a^2-4+3a\right)$

Concept Involved:

Distribute the binomial as first step, then distribute each term further, then group and combine like terms to get the final answer.

Calculation: Distribute the binomial $\left(1-2a\right)$

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

Distribute further

  $a^2-2a^3-4+8a+3a-6a^2$

Group like terms

  $-2a^3+a^2-6a^2+8a+3a-4$

Combine like terms

  $-2a^3-5a^2+11a-4$

Conclusion:

Multiplying $\left(1-2a\right)\left(a^2-4+3a\right)$ we end up getting $\boxed{-2a^3-5a^2+11a-4}$