Problem 32 Multiply. $$ -7 t^{2}\left(2... [FREE SOLUTION]

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Chapter 5: Problem 32

Multiply. $$ -7 t^{2}\left(2 t^{2}+t\right) $$

Short Answer

Expert verified

-14 t^{4} - 7 t^{3}

Step by step solution

- Distribute $-7 t^{2}$

Multiply \-7 t^{2}\ by each term inside the parentheses. This means distributing \-7 t^{2}\ across $2t^{2} + t$.

- Multiply \-7 t^{2}\ by \2 t^{2}\

Calculate the multiplication: $-7 t^{2} * 2 t^{2} = -14 t^{4} $.

- Multiply \-7 t^{2}\ by \ t\

Calculate the multiplication: $-7 t^{2} * t = -7 t^{3} $.

- Combine the results

Combine the results obtained in the previous steps to get: $-14 t^{4} - 7 t^{3} $.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Distributive Property

The Distributive Property is an essential mathematical rule. It helps us to simplify expressions and solve equations. Here's how we use it:

When you see an expression like $-7 t^{2}(2 t^{2}+t)$, it means you need to distribute $-7 t^{2}$ to each term inside the parentheses. This involves two main steps:

Step 1: Multiply $-7 t^{2}$ by the first term in the parentheses, which is $2 t^{2}$.
Step 2: Multiply $-7 t^{2}$ by the second term in the parentheses, which is \ t\.

This is like distributing items into groups, ensuring each group gets their share. By performing these operations, we distribute the multiplication over addition inside the parentheses. For example:

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91影视

Multiply. $$ -7 t^{2}\left(2 t^{2}+t\right) $$

Short Answer

Step by step solution

- Distribute \(-7 t^{2}\)

- Multiply \-7 t^{2}\ by \2 t^{2}\

- Multiply \-7 t^{2}\ by \ t\

- Combine the results

Key Concepts

Distributive Property

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