Question

The binomial expansion of (x-2y)^3 is ?

Answer 1

The binomial expansion of (x-2y)^3 using the binomial theorem is x^3 - 6x^2y + 12xy^2 - 8y^3.

Step-by-step explanation:

The binomial expansion of (x-2y)^3 can be calculated using the binomial theorem. According to the binomial theorem, for any term (a + b)^n, the expansion is given as a sum, which involves powers of a and b and binomial coefficients. Applying this formula to our expression, we get:

• x^3
• - 3(x^2)(2y)
• + 3(x)(2y)^2
• - (2y)^3

Combining these terms, the binomial expansion becomes x^3 - 6x^2y + 12xy^2 - 8y^3. This series is an accurate approximation for polynomial expressions raised to a power, and such expansions are integral in simplifying expressions in algebra.

Answer 2

x^3 - 6x^2y - 12xy^2 - 8y^3

Step-by-step explanation:

(x-2y)^3

There are three parts to binomial expansion - the coefficient, the power of the first term and the power of the second term.

Use Pascal's Triangle to find the coefficient.

^3 = 1 3 3 1

The first term's powers are descending:

x^3 x^2 x^1 x^0

The second term's powers are ascending.

-2y^0 -2y^1 -2y^2 -2y^3

The first coefficient is multiplied by the first power of the first term and the first power of the second term.

3C0 x^3 (-2y)^0 = 1 x^3 1 = x^3

2C1 x^2 (-2y)^1 = 3 x^2 -2y = -6x^2y

1C2 x^1 (-2y)^2 = 3 x -2y^2 = -12xy^2

0C3 x^0 (-2y)^3 = 1 1 -2y^3 = -8y^3