You are given that 2 2 2
2
ac
c bc with c ≠ 0. Show that 4b = 4c − a by filling in the blanks.
a. 2 2 2
2
ac
c bc a. Given
b. 4c2 = 4bc + ac b. __________________ and __________________
c. 4c = 4b + a c. __________________ and Distributive Property
d. __________________ d. Subtraction Property
e. 4b = 4c − a e. __________________
To show that 4b = 4c - a, let's follow the steps:
a. Given: 2^2 * 2 / 2 = 2(2 * ac / c) + a
b. Expanding the expression on the right side:
4c^2 / 2 = 4bc / 2 + ac
Simplifying:
2c^2 = 2bc + ac
Blank 1: Distributive Property
Blank 2: Simplifying
c. Bringing like terms together:
2c^2 - 2bc = ac
Blank 1: Subtraction Property
Blank 2: Distributive Property
d. Simplifying the equation:
2c(c - b) = ac
Blank: Subtraction Property
e. Dividing both sides by 2(c - b):
4b = 4c - a
Blank: Division Property
Therefore, we have shown that 4b = 4c - a.