Math Example--Polynomial Concepts--Binomial Theorem: Example 6

Topic

Polynomials

Description

Expand the binomial expression (x + 6)⁴. With n=4 in the binomial theorem, (x + y)⁴ = x⁴ + 4x³y + 6x²y² + 4xy³ + y⁴. Setting y = 6, the expanded expression is x⁴ + 24x³ + 216x² + 864x + 1296.

The binomial theorem allows students to expand binomials raised to powers efficiently. By breaking down the expansions through the theorem's formula, students can visualize and understand the patterns that emerge. Each example in this collection shows step-by-step applications of the binomial theorem to various powers, illustrating consistent rules and outcomes that reinforce comprehension of polynomial expansions.

Seeing multiple worked-out examples is essential for students to master mathematical concepts, particularly with the binomial theorem. By observing how each term builds upon previous steps, they can better grasp the structure and function of polynomial expansions, fostering a deeper understanding through repetition and pattern recognition.

Teacher's Script: Let's look at how we expand (x + 3)³ using the binomial theorem. Notice how each term involves increasing powers of x and decreasing powers of 3. By following the theorem's pattern, we find each term, which makes expanding powers more manageable. This step-by-step process helps us see how binomials expand when raised to a power.

For a complete collection of math examples related to Polynomials click on this link: Math Examples: The Binomial Theorem Collection.