Question

which statements are true about the fully simplified product of (b - 2c)(-3b + c)? select two options. the simplified product has 2 terms. the simplified product has 4 terms. the simplified product has a degree of 2. the simplified product has a degree of 4. the simplified product, in standard form, has exactly 2 negative terms.

Explanation:

Step1: Expand the product

Using the distributive property (FOIL method):
$$(b - 2c)(-3b + c) = b(-3b) + b(c) - 2c(-3b) - 2c(c)$$
$$= -3b^2 + bc + 6bc - 2c^2$$

Step2: Combine like terms

Combine the \( bc \) terms:
$$-3b^2 + (bc + 6bc) - 2c^2 = -3b^2 + 7bc - 2c^2$$

Step3: Analyze the simplified form

• Number of terms: The simplified product \( -3b^2 + 7bc - 2c^2 \) has 3 terms (so options about 2 or 4 terms are false).
• Degree: The highest power of variables is 2 (from \( b^2 \) or \( c^2 \)), so degree is 2 (true).
• Negative terms: In \( -3b^2 + 7bc - 2c^2 \), the terms \( -3b^2 \) and \( -2c^2 \) are negative (exactly 2 negative terms, true).

Answer:

The simplified product has a degree of 2.
The simplified product, in standard form, has exactly 2 negative terms.