(2x^5+3y^4)(-4x^2+9y^4)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (2x^5 + 3y^4)(-4x^2 + 9y^4)

This article will explore the process of expanding the given expression, (2x^5 + 3y^4)(-4x^2 + 9y^4). This type of expression involves multiplying two binomials, and we can use the distributive property (also known as FOIL - First, Outer, Inner, Last) to achieve the expansion.

Applying the Distributive Property

1. Multiply the First terms: (2x^5) * (-4x^2) = -8x^7

2. Multiply the Outer terms: (2x^5) * (9y^4) = 18x^5y^4

3. Multiply the Inner terms: (3y^4) * (-4x^2) = -12x^2y^4

4. Multiply the Last terms: (3y^4) * (9y^4) = 27y^8

Combining the Terms

Now, we add all the terms we obtained:

-8x^7 + 18x^5y^4 - 12x^2y^4 + 27y^8

Final Expanded Expression

Therefore, the expanded form of (2x^5 + 3y^4)(-4x^2 + 9y^4) is -8x^7 + 18x^5y^4 - 12x^2y^4 + 27y^8.