(5x%5E2%2B4x%2B7).jpeg "(2x-5)(5x^2+4x+7)")
Expanding the Expression: (2x-5)(5x^2+4x+7)
This article will guide you through expanding the expression (2x-5)(5x^2+4x+7) using the distributive property, also known as FOIL (First, Outer, Inner, Last).
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
In this case, we can think of (2x-5) as a single term, and we'll multiply it by each term within the second set of parentheses.
Expanding the Expression
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Multiply (2x-5) by the first term in the second set of parentheses (5x^2): (2x-5)(5x^2) = 10x^3 - 25x^2
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Multiply (2x-5) by the second term in the second set of parentheses (4x): (2x-5)(4x) = 8x^2 - 20x
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Multiply (2x-5) by the third term in the second set of parentheses (7): (2x-5)(7) = 14x - 35
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Add all the results together: 10x^3 - 25x^2 + 8x^2 - 20x + 14x - 35
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Combine like terms: 10x^3 - 17x^2 - 6x - 35
The Final Result
Therefore, the expanded form of the expression (2x-5)(5x^2+4x+7) is 10x^3 - 17x^2 - 6x - 35.