Question

Expansion of (3x - 4y)⁴ using binomial theorem.

Answer 1

The expansion of (3x - 4y)⁴ using the Binomial Theorem results in 81x⁴ - 432x³y + 864x²y² - 768xy³ + 256y⁴.

Step-by-step explanation:

The question asks for the expansion of the binomial expression (3x - 4y)⁴ using the Binomial Theorem. The binomial theorem states that (a + b)n can be expanded as a sum of terms in the form of nCk * a(n-k) * bk, where nCk represents the binomial coefficient. For the given expression, we will apply the theorem to fully expand it.

Here's the step-by-step expansion:

• The first term is (3x)4 and the coefficient is 1.
• The second term is 4(3x)3(-4y).
• The third term is 6(3x)2(-4y)2.
• The fourth term is 4(3x)(-4y)3.
• The final term is (-4y)4.

Calculating these terms using the binomial coefficients, the full expansion of (3x - 4y)⁴ is 81x⁴ - 432x³y + 864x²y² - 768xy³ + 256y⁴.