What is the answer to (a-b) x (a-b) =

 The expression \((a-b) \times (a-b)\) represents the square of the difference between two variables, \(a\) and \(b\). When you square a binomial, like \((a-b)\), you apply the formula for the square of a binomial, which is \((x-y)^2 = x^2 - 2xy + y^2\). This formula helps in expanding the expression by following specific algebraic rules, ensuring each term is correctly multiplied.

In the case of \((a-b) \times (a-b)\), you start by squaring the first term, \(a\), which gives \(a^2\). Next, you multiply the two terms, \(a\) and \(-b\), and double the product. This results in \(-2ab\). Finally, you square the second term, \(-b\), which gives \(b^2\). When these three components are combined, you get the fully expanded expression.

The final expanded expression is \(a^2 - 2ab + b^2\). This expression represents a perfect square trinomial, which is a common result in algebra when squaring a binomial. Each term in the trinomial has its significance: \(a^2\) is the square of the first term, \(-2ab\) is twice the product of the first and second terms, and \(b^2\) is the square of the second term.

Understanding how to expand \((a-b) \times (a-b)\) into \(a^2 - 2ab + b^2\) is crucial in algebra as it forms the foundation for more complex mathematical concepts. It demonstrates the importance of knowing algebraic identities and how they apply to different situations in mathematics, from simple equations to more advanced topics like polynomial expansions and solving quadratic equations.