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The 'difference of squares' concept is crucial in factoring specific types of polynomials. The term 'difference' here means subtraction. So, a difference of squares looks like this: a^2 - b^2
This is a subtraction between two squared terms.
In mathematical language, it holds that:a^2 - b^2 = (a - b)(a + b)
This formula states that any difference of squares can be factored into the product of two binomials.
Here’s an example for better understanding:
Consider the polynomial 9 - x^2.
You can see 9 is a square number (3^2) and x^2 is also a square term. Rewriting it to match the form a^2 - b^2, we get:3^2 - x^2 = (3 - x)(3 + x)
This factorization confirms the general rule for the difference of squares.

Algebraic expressions are combinations of numbers, variables, and operators (like addition or multiplication). Knowing how to handle algebraic expressions is fundamental for polynomial factoring.
Let's break down the polynomial given in the exercise: 64 - (r + 2t)^2
This expression includes:

• 64, a constant
• (r + 2t), a binomial squared

When factoring algebraic expressions, it's helpful to look for a common structure or pattern.
In this case, recognizing the difference of squares pattern allows us to proceed with factorization. Identifying such patterns simplifies the factoring process significantly.

Polynomial factoring involves breaking down a complex polynomial into simpler products of factors or binomials. This technique is essential in algebra to simplify expressions and solve equations.
The given polynomial, 64 - (r + 2t)^2, exploits the difference of squares concept. Here’s how we do it step-by-step:
1. Identify the squares: 64 = 8^2 and (r + 2t)^2.
2. Rewrite the polynomial as a difference of squares: a^2 - b^2.
Here, a = 8 and b = (r + 2t). Substituting these values, you get: 8^2 - (r + 2t)^2.
3. Apply the difference of squares factoring formula: 8^2 - (r + 2t)^2 = (8 - (r + 2t))(8 + (r + 2t)).
4. Simplify the factored form: (8 - r - 2t)(8 + r + 2t)
This is the fully factored form of the polynomial. Each step of breaking down the polynomial leverages recognizing patterns and applying the appropriate algebraic rules.