Question

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 (-3y^2 + 7y - 9). the final simplified product is (-3y^2 + 37y - 84).

Explanation:

Step1: Expand $(y-5)^2$

$(y-5)^2 = y^2 -10y +25$

Step2: Distribute -3 to the expanded terms

$-3(y^2 -10y +25) = -3y^2 +30y -75$

Step3: Combine like terms with remaining terms

$-3y^2 +30y -75 -9 +7y = -3y^2 +37y -84$

Step4: Evaluate each statement

1. First step is not distributing -3 (must expand $(y-5)^2$ first): False
2. Simplified product has 3 terms: True
3. Simplified product is degree 2 (not 3): False
4. Final product is $-3y^2 +7y -9$: False
5. Final product is $-3y^2 +37y -84$: True

Answer:

• There are 3 terms in the simplified product.
• The final simplified product is $-3y^2 + 37y - 84$.