Final answer:
To expand the expression (2x^4+3x^3)(2x^4-3x^3), we use the distributive property to multiply each term in the first parenthesis by each term in the second, then combine the like terms, resulting in 4x^8 - 9x^6.
Step-by-step explanation:
To expand and combine like terms for the expression (2x4+3x3)(2x4-3x3), we will apply the distributive property, also known as the FOIL method for binomials. We multiply each term in the first parenthesis with each term in the second parenthesis:
- (2x4)×(2x4) = 4x8
- (2x4)×(-3x3) = -6x7
- (3x3)×(2x4) = 6x7
- (3x3)×(-3x3) = -9x6
The next step is to combine like terms. In this case, the -6x7 and 6x7 are like terms and will cancel each other out:
- 4x8 - 6x7 + 6x7 - 9x6 = 4x8 - 9x6
Therefore, the expanded form of the given expression is 4x8 - 9x6.