Expanding the expression (2a-6)^3 can be done using the binomial theorem or by using the distributive property repeatedly. Here, I will show both methods:
Using the binomial theorem:
(2a-6)^3 = C(3, 0)(2a)^3(-6)^0 + C(3, 1)(2a)^2(-6)^1 + C(3, 2)(2a)^1(-6)^2 + C(3, 3)(2a)^0(-6)^3
Simplifying each term:
= 1(8a^3)(1) + 3(4a^2)(-6) + 3(2a)(36) + 1(1)(-216)
= 8a^3 - 72a^2 + 216a - 216
Using the distributive property repeatedly:
(2a-6)^3 = (2a-6)(2a-6)(2a-6)
Expanding the first two binomials using the distributive property:
= (4a^2 - 12a - 12a + 36)(2a-6)
= (4a^2 - 24a + 36)(2a-6)
Expanding the product of the two binomials:
= 8a^3 - 48a^2 + 72a - 24a^2 + 144a - 216
= 8a^3 - 72a^2 + 216a - 216
Both methods give us the same expanded expression:
(2a-6)^3 = 8a^3 - 72a^2 + 216a - 216
expand- (2a-6)^3
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