Question

are the expressions $4f + (-21) + 10f$ and $-7(-2f + 3)$ equivalent? show why or why not.
first combine the like terms in $4f + (-21) + 10f$.
$4f + (-21) + 10f = 14f + (-21)$
which factored expressions are equivalent to $14f + (-21)$?
choose all that apply.
$-7(2f - 3)$ $-7(-2f + 3)$ $7(2f - 3)$ $7(-2f - 3)$

Explanation:

Step1: Simplify first expression

Combine like terms:
$4f + (-21) + 10f = (4f + 10f) + (-21) = 14f - 21$

Step2: Factor the simplified expression

Factor out the greatest common factor 7:
$14f - 21 = 7(2f - 3)$

Step3: Verify the second expression

Expand $-7(-2f + 3)$ using distribution:
$-7(-2f + 3) = (-7)(-2f) + (-7)(3) = 14f - 21$

Step4: Check factored options

Test each option by expanding:

1. $-7(2f - 3) = -14f + 21$ (not equivalent)
2. $-7(-2f + 3) = 14f - 21$ (equivalent)
3. $7(2f - 3) = 14f - 21$ (equivalent)
4. $7(-2f - 3) = -14f - 21$ (not equivalent)

Answer:

The expressions $4f + (-21) + 10f$ and $-7(-2f + 3)$ are equivalent, since both simplify to $14f - 21$.
The equivalent factored expressions are:

• $-7(-2f + 3)$
• $7(2f - 3)$