(3x%E2%88%929).jpeg "(2x−10)(3x−9)")
Factoring and Expanding the Expression (2x−10)(3x−9)
This article will explore the algebraic expression (2x−10)(3x−9), focusing on how to factor and expand it.
Factoring the Expression
Factoring an expression means rewriting it as a product of simpler expressions. To factor (2x−10)(3x−9), we can start by looking for common factors within each of the parentheses:
- (2x−10) has a common factor of 2: 2(x-5)
- (3x−9) has a common factor of 3: 3(x-3)
Now we can rewrite the original expression as: (2x−10)(3x−9) = 2(x-5) * 3(x-3)
This further simplifies to: 6(x-5)(x-3)
Expanding the Expression
Expanding an expression means multiplying out all the terms. To expand (2x−10)(3x−9), we can use the FOIL method:
- First: Multiply the first terms of each binomial: 2x * 3x = 6x²
- Outer: Multiply the outer terms of each binomial: 2x * -9 = -18x
- Inner: Multiply the inner terms of each binomial: -10 * 3x = -30x
- Last: Multiply the last terms of each binomial: -10 * -9 = 90
Adding all the results together gives us: 6x² - 18x - 30x + 90
Finally, combining like terms, we get the expanded form: 6x² - 48x + 90
Summary
We have explored both factoring and expanding the expression (2x−10)(3x−9). The factored form is 6(x-5)(x-3), while the expanded form is 6x² - 48x + 90. Understanding these concepts is crucial for simplifying and manipulating algebraic expressions.