Multiplying Polynomials and Simplifying Expressions
Question 79072 • FL-1200700-Mathematics for College Algebra MIS
Consider the expression –3(y – 5)2 – 9 + 7y.Which statements are true about the process and simplified product? Check all that apply.The first step in simplifying is to distribute the –3 throughout the parentheses.There are 3 terms in the simplified product.The simplified product is a degree 3 polynomial.The final simplified product is –3y2 + 7y – 9.The final simplified product is –3y2 + 37y – 84.
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. Multiplying by −3 and combining the remaining terms gives −3y² + 30y − 75 − 9 + 7y = −3y² + 37y − 84. This has three terms, so statements B and E are true; its degree is 2, and the exponent means you cannot first distribute −3 through the unsquared binomial as stated in A.
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