9
AssignmentMultiple Select

Multiplying Polynomials and Simplifying Expressions

Question 9 • 26MATH_Recovery_Alg1B22

Consider the expression –3(y – 5)2 – 9 + 7y.Which statements are true about the process and simplified product? Check all that apply.

Answer
A
The first step in simplifying is to distribute the –3 throughout the parentheses.
B
There are 3 terms in the simplified product.
C
The simplified product is a degree 3 polynomial.
D
The final simplified product is –3y2 + 7y – 9.
E
The final simplified product is –3y2 + 37y – 84.

Explanation

First square the binomial: (y − 5)² = y² − 10y + 25. Then multiply by −3 and combine like terms: −3y² + 30y − 75 − 9 + 7y = −3y² + 37y − 84. This has three terms, so B is true, and it matches choice E. The polynomial has degree 2, not degree 3; also, the exponent means you square the binomial before multiplying by −3.

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