Final answer:
To expand the expression (1 - 3x)⁴ using the binomial theorem, we can use the formula (a + b)ⁿ = C(n,0)aⁿb⁰ + C(n,1)aⁿ⁻¹b¹ + C(n,2)aⁿ⁻²b² + ... + C(n,n-1)abⁿ⁻¹ + C(n,n)a⁰bⁿ. In this case, a = 1, b = -3x, and n = 4. Plugging these values into the formula, we get (1 - 3x)⁴ = 1 - 12x + 54x² - 108x³ + 81x⁴.
Step-by-step explanation:
To expand the expression (1 - 3x)⁴ using the binomial theorem, we can use the formula:
(a + b)ⁿ = C(n,0)aⁿb⁰ + C(n,1)aⁿ⁻¹b¹ + C(n,2)aⁿ⁻²b² + ... + C(n,n-1)abⁿ⁻¹ + C(n,n)a⁰bⁿ
In this case, a = 1, b = -3x, and n = 4. Plugging these values into the formula, we get:
(1 - 3x)⁴ = C(4,0)1⁴(-3x)⁰ + C(4,1)1³(-3x)¹ + C(4,2)1²(-3x)² + C(4,3)1¹(-3x)³ + C(4,4)1⁰(-3x)⁴
Simplifying this expression gives:
(1 - 3x)⁴ = 1 - 12x + 54x² - 108x³ + 81x⁴
Combining these, we have the expanded form: 1 - 12x + 54x² - 108x³ + 81x⁴.