(2v^2+3x^2)(2v^2+3x^2)

2 min read Jun 16, 2024
(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:

  1. (2v^2 + 3x^2)(2v^2 + 3x^2) = (2v^2 + 3x^2)(2v^2) + (2v^2 + 3x^2)(3x^2)
  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).

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