(t+3)(t^2+4t+7)

2 min read Jun 16, 2024
(t+3)(t^2+4t+7)

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

  1. 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)

  2. 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

  3. 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.

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