Question

Which statements are true about the fully simplified product of (b minus 2 c)(negative 3 b + 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.

Answer 1

The simplified product has a degree of 2.

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

Step-by-step explanation:

(b - 2c)(-3b + c)

= b(-3b) + bc + (-2c)(-3b) + (-2c) (c)

= -3b² + bc + 6bc - 2c²

= -3b² + 7bc - 2c²

Hence, the simplified product has a degree of 2.

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

Answer 2

Given:

(b minus 2 c)(negative 3 b + c)

To find:

Which statements are true about the fully simplified product of (b minus 2 c)(negative 3 b + c)?

Solution:

From given, we have 2 equations,

(b minus 2 c) and (negative 3 b + c)

⇒ (b - 2c) and (-3b + c)

Their product is given by as follows,

(b - 2c) × (-3b + c)

= b (-3b) + bc + (-2c) (-3b) + (-2c) (c)

= -3b² + bc + 6bc - 2c²

= -3b² + 7bc - 2c²

Therefore,

The simplified product has a degree of 2.

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