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Expanding the Expression (t+3)(t^2+4t+7)
This article will guide you through the process of expanding the expression (t+3)(t^2+4t+7) using the distributive property.
Understanding the Distributive Property
The distributive property states that to multiply a sum by a number, you can multiply each term in the sum by the number and then add the products.
Expanding the Expression
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Distribute (t+3) over the first term of the second expression (t^2): (t+3)(t^2+4t+7) = t(t^2+4t+7) + 3(t^2+4t+7)
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Distribute (t+3) over the second term of the second expression (4t): t(t^2+4t+7) + 3(t^2+4t+7) = t^3 + 4t^2 + 7t + 3t^2 + 12t + 21
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Distribute (t+3) over the third term of the second expression (7): t^3 + 4t^2 + 7t + 3t^2 + 12t + 21 = t^3 + 7t^2 + 19t + 21
Simplified Expression
The expanded and simplified expression is t^3 + 7t^2 + 19t + 21.
Conclusion
By applying the distributive property, we successfully expanded the expression (t+3)(t^2+4t+7) into a polynomial with four terms: t^3 + 7t^2 + 19t + 21.