Question

I’m not quite sure how to answer this question. Excuse the pencil marks this is from an assignment I didn’t do so well on so I’m trying to understand what I did wrong

Answer 1

Given the expressions:

$\begin{gathered} (8x-1)(4x^2+9) \\ \\ 32x^3-4x^2+72x-9 \end{gathered}$

You can multiply the binomials of the first expression in order to expand it. You can use the FOIL Method to multiply them, which states that:

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

You also need to remember the Sign Rules for Multiplication:

$\begin{gathered} +\cdot+=+ \\ -\cdot-=+ \\ -\cdot+=- \\ +\cdot-=- \end{gathered}$

Then:

$=(8x)(4x^2)+(8x)(9)-(1)(4x^2)-(1)(9)$$=32x^3+72x-4x^2-9$$=32x^3-4x^2+72x-9$

By definition, Equivalent Expressions work the same, but they have different forms.

Since:

$(8x-1)(4x^2+9)=32x^3-4x^2+72x-9$

You can conclude that they are Equivalent Expressions.

Hence, the answer is: They are Equivalent Expression, because:

$(8x-1)(4x^2+9)=32x^3-4x^2+72x-9$