Question

write an equivalent expression.
5y - 10
select all that apply
a. 5(y - 2)
b. 5(y - 10)
c. (y - 2)5
d. 5(5y - 2)

Explanation:

Step1: Factor out 5 from \(5y - 10\)

We use the distributive property \(ab - ac = a(b - c)\). Here, \(a = 5\), \(b = y\), \(c = 2\) (since \(10 = 5\times2\)). So, \(5y - 10 = 5(y - 2)\).

Step2: Check option A

Option A is \(5(y - 2)\), which matches the factored form we got.

Step3: Check option B

Option B is \(5(y - 10)\). Expanding it: \(5\times y - 5\times10 = 5y - 50\), which is not equal to \(5y - 10\).

Step4: Check option C

Option C is \((y - 2)5\). Multiplication is commutative, so \((y - 2)5 = 5(y - 2)\), which is equivalent to \(5y - 10\).

Step5: Check option D

Option D is \(5(5y - 2)\). Expanding it: \(5\times5y - 5\times2 = 25y - 10\), which is not equal to \(5y - 10\).

Answer:

A. \(5(y - 2)\), C. \((y - 2)5\)