Algebra Expansion of (a + b)³

Expansion of $(a + b)³$

• The expanded form of $(a + b)³$ is given by the formula: [(a + b)³ = a³ + 3a²b + 3ab² + b³]
• This expansion involves combining terms with varying powers of (a) and (b).

Term Representing the Product of $a$ and $b$

• The term in the expansion that represents the product of (a) and (b) is (3a²b).
• This term indicates that (a) is squared while (b) appears linearly, embodying their mixed product.

Coefficient of the $a²b$ Term

• The coefficient of the (a²b) term in the expansion is (3).
• This reflects how many ways we can select one (b) from the three total factors of ((a + b)) when expanding.

Value of $(a + b)³$ When (a = 1) and (b = 1)

• If (a = 1) and (b = 1), then: [(1 + 1)³ = 2³ = 8]
• This demonstrates the calculation of the cubic expansion at specific input values.

Valid Application of $(a + b)³$

• The expression $(a + b)³$ can be applied in various algebraic contexts, including polynomial expansions, binomial theorem applications, and combinatorial problems.
• It proves useful in solving real-world problems involving volume calculations when combining different quantities.