3
QuizMultiple Choice

Multiplying Polynomials and Simplifying Expressions — Quiz

Question 3 • Algebra I

Simplify the expression 3 x open paren x minus 12 x close paren plus 3 x squared minus 2 times open paren x minus 2 close paren squared Which statements are true about the process and simplified product? Choose three correct answers.

Answer
A
The term negative 2 times open paren x minus 2 close paren squared is simplified by first squaring the expression x minus 2 .
B
The final simplified product is negative 28 x squared plus 8 x minus 8 .
C
After multiplying, the like terms are combined by adding and subtracting.
D
The simplified product is a binomial.
E
The parentheses are eliminated through multiplication.

Explanation

First square the binomial: (x − 2)² = x² − 4x + 4, then multiply by −2 to get −2x² + 8x − 8. Also, 3x(x − 12x) = −33x², so the full expression becomes −33x² + 3x² − 2x² + 8x − 8. Multiplying removes the parentheses, and combining like terms gives −32x² + 8x − 8. Thus the expression is a trinomial, not a binomial, and choice D has the wrong x² coefficient.

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