Problem 56 Add or subtract, as indicated. ... [FREE SOLUTION]

Chapter 15: Problem 56

Add or subtract, as indicated. $$ \left(4 t^{2}+6 t-7\right)-(t+5) $$

Short Answer

Expert verified

$4t^2 + 5t - 12$

Step by step solution

- Distribute the Negative Sign

Rewrite the equation by distributing the negative sign to each term inside the parentheses for the second polynomial. This means changing the signs of each term in $t + 5$. The equation becomes: $4t^2 + 6t - 7 - t - 5$.

- Combine Like Terms

Group and combine the like terms. Like terms are terms that contain the same variables raised to the same power. Here, combine $6t$ and $-t$, and then combine the constants $-7$ and $-5$: $4t^2 + (6t - t) + (-7 - 5)$.

- Simplify the Expression

Simplify the expression by performing the arithmetic operations: $6t - t = 5t$ and $-7 - 5 = -12$. The simplified expression becomes: $4t^2 + 5t - 12$.

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Key Concepts

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

Distribute Negative Sign

To start, we need to address the subtraction of an entire polynomial. This involves distributing the negative sign to each term inside the parentheses. In our example, we have:
$4t^{2} + 6t - 7 - (t + 5)$.
Distributing the negative sign means changing the signs of each term in the second polynomial.

So, $t + 5$ turns into $-t - 5$.
Now the equation looks like this: $4t^{2} + 6t - 7 - t - 5 $.

This step lays the foundation for combining like terms.

Combine Like Terms

Next, our goal is to combine like terms. Like terms are terms that have the same variable raised to the same power. Let's break this down:

$4t^{2}$ is a term by itself as there are no other $t^{2}$ terms to combine with.
$6t$ and $-t$ both have the variable $t$, so they are like terms.
The constants, $-7$ and $-5$, are also like terms.

We rewrite the expression grouping these like terms: $4t^{2} + (6t - t) + (-7 - 5)$.

Simplify Expression

Finally, we simplify by performing the arithmetic operations:

Combine $6t$ and $-t$ to get $6t - t = 5t$.
Then, combine the constants $-7$ and $-5$ to get $-7 - 5 = -12$.

This gives us the simplified expression: $4t^{2} + 5t - 12$.

By following these steps, we have successfully simplified our polynomial expression. This method can be applied to any polynomial addition or subtraction problem you encounter!

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91影视

Add or subtract, as indicated. $$ \left(4 t^{2}+6 t-7\right)-(t+5) $$

Short Answer

Step by step solution

- Distribute the Negative Sign

- Combine Like Terms

- Simplify the Expression

Key Concepts

Distribute Negative Sign

Combine Like Terms

Simplify Expression

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