Answer:
The difference of two squares can be simplified using the formula \((a + b)(a - b)\).
Explanation:
The difference of two squares refers to the algebraic expression that results when you subtract one perfect square from another. It can be simplified using a special formula.
The formula for the difference of two squares is:
\(a^2 - b^2 = (a + b)(a - b)\)
Let's break this down step-by-step with an example. Suppose we have the expression \(x^2 - 4\). To simplify it using the difference of two squares formula, we need to find two numbers whose squares add up to \(x^2\) and 4, respectively.
In this case, \(x^2\) can be written as \((x)^2\) and 4 as \((2)^2\). So, the expression becomes:
\(x^2 - 4 = (x + 2)(x - 2)\)
Notice that we have factored the expression into two binomials: \(x + 2\) and \(x - 2\). These binomials are conjugates of each other.
Now let's try another example. Consider the expression \(9y^2 - 25\). Using the formula, we find that:
\(9y^2 - 25 = (3y + 5)(3y - 5)\)
In this case, we identified the squares as \(9y^2\) and \(25\), which are the squares of \(3y\) and \(5\) respectively.
To summarize, the difference of two squares can be simplified using the formula \((a + b)(a - b)\). This formula allows us to factor the expression into two binomials, which are conjugates of each other. By identifying the squares within the expression, we can apply the formula and simplify the expression.