(2v%5E2%2B3x%5E2).jpeg "(2v^2+3x^2)(2v^2+3x^2)")
Expanding the Expression (2v^2 + 3x^2)(2v^2 + 3x^2)
This expression represents the product of two identical binomials. To expand it, we can use the FOIL method (First, Outer, Inner, Last), or the distributive property.
Using the FOIL Method
- First: (2v^2)(2v^2) = 4v^4
- Outer: (2v^2)(3x^2) = 6v^2x^2
- Inner: (3x^2)(2v^2) = 6v^2x^2
- Last: (3x^2)(3x^2) = 9x^4
Combining the terms, we get:
4v^4 + 6v^2x^2 + 6v^2x^2 + 9x^4
Simplifying by combining like terms:
4v^4 + 12v^2x^2 + 9x^4
Using the Distributive Property
The distributive property states that a(b + c) = ab + ac. We can apply this twice to expand the expression:
- (2v^2 + 3x^2)(2v^2 + 3x^2) = (2v^2 + 3x^2)(2v^2) + (2v^2 + 3x^2)(3x^2)
- = 4v^4 + 6v^2x^2 + 6v^2x^2 + 9x^4
Again, combining like terms gives us:
4v^4 + 12v^2x^2 + 9x^4
Conclusion
Both methods result in the same expanded expression: 4v^4 + 12v^2x^2 + 9x^4. This expression is a trinomial (an expression with three terms) and represents the perfect square of the binomial (2v^2 + 3x^2).