Complete Question:
Emily and Zach have two different polynomials to multiply: Polynomial product A: (4x2 – 4x)(x2 – 4) Polynomial product B: (x2 + x – 2)(4x2 – 8x) They are trying to determine if the products of the two polynomials are the same. But they disagree about how to solve this problem.
Answer:
Step-by-step explanation:
<em>See comment for complete question</em>
Given
Required
Determine how they can show if the products are the same or not
To do this, we simply factorize each polynomial
For, Polynomial A: We have:
Factor out 4x
Apply difference of two squares on x^2 - 4
For, Polynomial B: We have:
Expand x^2 + x - 2
Factorize:
Factor out x + 2
Factor out 4x
Rearrange
The simplified expressions are:
and
Hence, both polynomials are equal