(5x-6)%2B8.jpeg "(2x-3)(5x-6)+8")
Expanding and Simplifying the Expression: (2x-3)(5x-6)+8
In this article, we will explore how to simplify the expression (2x-3)(5x-6)+8. This involves expanding the product of the binomials and then combining like terms.
Expanding the Binomial Product
We can expand the product of the binomials using the FOIL method, which stands for First, Outer, Inner, Last. This method helps us systematically multiply each term in the first binomial with each term in the second binomial.
- First: Multiply the first terms of each binomial: (2x)(5x) = 10x²
- Outer: Multiply the outer terms of the binomials: (2x)(-6) = -12x
- Inner: Multiply the inner terms of the binomials: (-3)(5x) = -15x
- Last: Multiply the last terms of each binomial: (-3)(-6) = 18
Now, we have: (2x-3)(5x-6) = 10x² -12x -15x + 18
Combining Like Terms
We can combine the terms with the same variable and exponent: 10x² -12x -15x + 18 = 10x² - 27x + 18
Final Simplification
Finally, we add the constant term: 10x² - 27x + 18 + 8 = 10x² - 27x + 26
Therefore, the simplified form of the expression (2x-3)(5x-6)+8 is 10x² - 27x + 26.
This expression is now in its simplest form, and we can use it for further calculations or analysis.