Question

combining like terms with negative coefficients & distribution
simplify to create an equivalent expression.
-k + 2(-2k - 5)
choose 1 answer
a -3k + 10
b -5k - 10
c -5k + 10
d -3k - 10

Explanation:

Step1: Distribute the 2

We use the distributive property \(a(b + c)=ab+ac\). Here, \(a = 2\), \(b=-2k\), and \(c = - 5\). So, \(2(-2k-5)=2\times(-2k)+2\times(-5)=-4k - 10\). The expression becomes \(-k-4k - 10\).

Step2: Combine like terms

The like terms are \(-k\) and \(-4k\). Combining them: \(-k-4k=(-1 - 4)k=-5k\). So the simplified expression is \(-5k-10\).

Answer:

B. \(-5k - 10\)