(2a2+7a−10)(a−5)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (2a² + 7a − 10)(a − 5)

This article will explore the expansion of the expression (2a² + 7a − 10)(a − 5) using the distributive property.

The Distributive Property

The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

We can use this property to expand our expression.

Expanding the Expression

1. Multiply the first term of the first factor by each term of the second factor:

   (2a²)(a) + (2a²)(-5)

   This gives us 2a³ - 10a²

2. Multiply the second term of the first factor by each term of the second factor:

   (7a)(a) + (7a)(-5)

   This gives us 7a² - 35a

3. Multiply the third term of the first factor by each term of the second factor:

   (-10)(a) + (-10)(-5)

   This gives us -10a + 50

4. Combine all the resulting terms:

   2a³ - 10a² + 7a² - 35a - 10a + 50

5. Simplify by combining like terms:

   2a³ - 3a² - 45a + 50

Conclusion

Therefore, the expanded form of the expression (2a² + 7a − 10)(a − 5) is 2a³ - 3a² - 45a + 50.