(x%2B5)-as-an-equivalent-trinomial.jpeg "(x+5)(x+5) As An Equivalent Trinomial")
Expanding (x+5)(x+5) into an Equivalent Trinomial
The expression (x+5)(x+5) is a binomial multiplied by itself, which is also known as squaring a binomial. To find the equivalent trinomial, we can use the FOIL method:
First: Multiply the first terms of each binomial: x * x = x² Outer: Multiply the outer terms of the binomials: x * 5 = 5x Inner: Multiply the inner terms of the binomials: 5 * x = 5x Last: Multiply the last terms of each binomial: 5 * 5 = 25
Now, combine the terms: x² + 5x + 5x + 25
Finally, simplify by combining the like terms: x² + 10x + 25
Therefore, the equivalent trinomial for (x+5)(x+5) is x² + 10x + 25.
Key Points:
- Squaring a binomial: (a + b)² = a² + 2ab + b²
- FOIL method: A helpful tool for expanding binomials.
- Combining like terms: Simplifying expressions by adding or subtracting terms with the same variable and exponent.
By understanding these concepts, you can easily expand any binomial squared into its equivalent trinomial form.