(2x-4).jpeg "(3x+1)(2x-4)")
Expanding and Simplifying the Expression (3x+1)(2x-4)
In mathematics, we often encounter expressions that involve multiplying binomials. One such expression is (3x+1)(2x-4). To understand and manipulate this expression effectively, we need to expand it and simplify it.
Expanding the Expression
We can expand the expression using the FOIL method:
- First: Multiply the first terms of each binomial: (3x)(2x) = 6x²
- Outer: Multiply the outer terms of the binomials: (3x)(-4) = -12x
- Inner: Multiply the inner terms of the binomials: (1)(2x) = 2x
- Last: Multiply the last terms of each binomial: (1)(-4) = -4
Combining these terms, we get: 6x² - 12x + 2x - 4
Simplifying the Expression
Next, we can simplify the expression by combining like terms:
6x² - 10x - 4
Conclusion
By expanding and simplifying the expression (3x+1)(2x-4), we arrive at the simplified form 6x² - 10x - 4. This process involves applying the FOIL method and combining like terms. This technique is crucial for solving various mathematical problems involving polynomials.