Question

Simplify to create an equivalent expression: −4(z−3)−4(5−4z)

a) −24z−32
b) 12z+8
c) 12z−321
d) 12z+32

Answer 1

To simplify the given expression, distribute -4 into both sets of parentheses and combine like terms, resulting in the simplified expression 12z - 8.

Step-by-step explanation:

To simplify the expression −4(z−3)−4(5−4z), we distribute the -4 into each parenthesis:

• −4 × z = −4z
• −4 × (−3) = +12
• −4 × 5 = −20
• −4 × (−4z) = +16z

Combining all the terms, we get −4z + 12 − 20 + 16z.

Now, combine like terms (−4z and +16z):

• (−4z + 16z) = 12z
• (+12 − 20) = −8

Finally, add the results of the like terms to get the simplified expression:

12z − 8, which corresponds to option (b) 12z + 8.