Question

4. Multiply the two polynomials using the destructive property.5. Are the two products the same when you multiply them horizontally?4. A)

Answer 1

Given:

$(4x^2-4x)(x^2-4)$

To multiply the two polynomials using the distributive property, we first follow the rule shown below:

For: (a+b)(c+d)=a(c+d)+b(c+d)=ac+ad+bc+bd

We let:

$\begin{gathered} a=4x^2 \\ b=-4x \\ c=x^2 \\ d=-4 \end{gathered}$

Now, we plug in what we know:

$\begin{gathered} (4x^{2}-4x)(x^{2}-4) \\ =(4x^2)(x^2)+(4x^2)(-4)+(-4x)(x^2)+(-4x)(-4) \\ Simplify\text{ and rearrange} \\ =4x^4-16x^2-4x^3+16x \\ =4x^4-4x^3-16x^2+16x \end{gathered}$

Therefore, the answer is:

$=4x^4-4x^3-16x^2+16x$