(2x%5E2%2B4x).jpeg "(x^2+x-6)(2x^2+4x)")
Expanding and Simplifying the Expression (x^2 + x - 6)(2x^2 + 4x)
This article will guide you through the process of expanding and simplifying the given expression: (x^2 + x - 6)(2x^2 + 4x).
Understanding the Steps
To expand and simplify this expression, we will use the distributive property (also known as FOIL). This means we will multiply each term in the first set of parentheses by each term in the second set of parentheses.
Expanding the Expression
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Multiply x^2 from the first set by each term in the second set:
- x^2 * 2x^2 = 2x^4
- x^2 * 4x = 4x^3
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Multiply x from the first set by each term in the second set:
- x * 2x^2 = 2x^3
- x * 4x = 4x^2
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Multiply -6 from the first set by each term in the second set:
- -6 * 2x^2 = -12x^2
- -6 * 4x = -24x
Combining Like Terms
Now we have: 2x^4 + 4x^3 + 2x^3 + 4x^2 - 12x^2 - 24x
Combine like terms:
- 2x^4 remains unchanged.
- 4x^3 + 2x^3 = 6x^3
- 4x^2 - 12x^2 = -8x^2
- -24x remains unchanged.
Simplified Expression
The simplified expression is 2x^4 + 6x^3 - 8x^2 - 24x.
Conclusion
By using the distributive property and combining like terms, we have successfully expanded and simplified the expression (x^2 + x - 6)(2x^2 + 4x) to 2x^4 + 6x^3 - 8x^2 - 24x.