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Here are the binomial expansions for each expression:

1. \((2x + y)^4 = 16x^4 + 32x^3y + 24x^2y^2 + 8xy^3 + y^4\)

2. \((z - 3)^5 = z^5 - 15z^4 + 90z^3 - 270z^2 + 405z - 243\)

3. \((1 - 2x)^6 = 64x^6 - 192x^5 + 240x^4 - 160x^3 + 60x^2 - 12x + 1\)

Would you like further details or have any questions about these expansions?

Here are 5 follow-up questions for further exploration:
1. Can you apply the binomial theorem to expand \((3x - 2)^4\)?
2. What is the general formula for expanding \((a + b)^n\) using binomial expansion?
3. How would the expansion differ for a binomial raised to an odd power?
4. What is the role of binomial coefficients in these expansions?
5. Can you apply binomial expansion to expand a term like \((x^2 + 1)^3\)?

**Tip:** Binomial expansion relies on the binomial theorem, where each term involves binomial coefficients (from Pascal's Triangle) multiplied by powers of each variable.

Expand the following using the formula of binomial expansion: (2x + y)^4, (z - 3)^5, (1 - 2x)^6

Expand the binomials (2x + y)^4, (z - 3)^5, and (1 - 2x)^6 using the binomial theorem. Learn how to apply binomial expansion formulas, use binomial coefficients from Pascal's Triangle, and solve algebraic expressions with powers. Suitable for high school students in Grades 10-12.

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