(5a%5E2-2ab%5E2-b).jpeg "(-6a^3b+2ab^2)(5a^2-2ab^2-b)")
Expanding the Expression: (-6a^3b + 2ab^2)(5a^2 - 2ab^2 - b)
This article will guide you through the process of expanding the given algebraic expression: (-6a^3b + 2ab^2)(5a^2 - 2ab^2 - b).
Understanding the Problem
We are dealing with the multiplication of two binomials. To expand this expression, we need to distribute each term of the first binomial to every term of the second binomial. This process is often referred to as FOIL (First, Outer, Inner, Last), but it's important to remember that FOIL only applies to the multiplication of two binomials. Here, we have a trinomial in the second set of parentheses.
The Steps to Expansion
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Distribute the first term of the first binomial:
- -6a^3b * 5a^2 = -30a^5b
- -6a^3b * -2ab^2 = 12a^4b^3
- -6a^3b * -b = 6a^3b^2
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Distribute the second term of the first binomial:
- 2ab^2 * 5a^2 = 10a^3b^2
- 2ab^2 * -2ab^2 = -4a^2b^4
- 2ab^2 * -b = -2ab^3
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Combine all the terms: -30a^5b + 12a^4b^3 + 6a^3b^2 + 10a^3b^2 - 4a^2b^4 - 2ab^3
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Simplify by combining like terms: -30a^5b + 12a^4b^3 + 16a^3b^2 - 4a^2b^4 - 2ab^3
Conclusion
Therefore, the expanded form of the expression (-6a^3b + 2ab^2)(5a^2 - 2ab^2 - b) is -30a^5b + 12a^4b^3 + 16a^3b^2 - 4a^2b^4 - 2ab^3.
This process can be used to expand any algebraic expression involving the multiplication of polynomials. Remember to carefully distribute each term and combine like terms to arrive at the simplified expanded form.