x(2x-7).jpeg "(7-2x)x(2x-7)")
Simplifying the Expression (7-2x)x(2x-7)
The expression (7-2x)x(2x-7) can be simplified through a few steps involving basic algebra. Let's break down the process:
1. Recognizing the Pattern
Notice that the two factors are almost identical, except for the order of the terms. We have (7-2x) and (2x-7), which are essentially the same expression with reversed signs.
2. Using the Commutative Property
The commutative property of multiplication allows us to rearrange the order of factors without affecting the result. Therefore, we can rewrite the expression as:
(7-2x) x (2x-7) = (2x-7) x (7-2x)
3. Applying the Difference of Squares Pattern
Now, we see a classic algebraic pattern: the difference of squares. This pattern states that:
(a-b) x (a+b) = a² - b²
In our expression, a = 2x and b = 7. Applying the pattern, we get:
(2x-7) x (7-2x) = (2x)² - (7)²
4. Simplifying
Simplifying the squares, we have:
(2x)² - (7)² = 4x² - 49
Therefore, the simplified form of the expression (7-2x)x(2x-7) is 4x² - 49.