Question

Use algebra tiles to find (6x2+9x)+(7x2+x+8).
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Combine like terms. For example, write 3 instead of 1 + 1 + 1.

Answer 1

To solve \((6x^2 + 9x) + (7x^2 + x + 8)\) using algebra tiles, let's first break down how many tiles we have for each term.

1. **Count the \( x^2 \) tiles:**
- From \( 6x^2 \): 6 tiles
- From \( 7x^2 \): 7 tiles
- Total: \( 6 + 7 = 13 \) tiles of \( x^2 \)

2. **Count the \( x \) tiles:**
- From \( 9x \): 9 tiles
- From \( x \): 1 tile
- Total: \( 9 + 1 = 10 \) tiles of \( x \)

3. **Count the constant (1) tiles:**
- There’s a constant term of \( 8 \).
- Total: 8 tiles of 1.

Now, we can combine all of this information:

- The \( x^2 \) terms combine to give us \( 13x^2 \).
- The \( x \) terms combine to give us \( 10x \).
- The constants combine to give us \( + 8 \).

Putting it all together, we write the combined expression as:

\[
13x^2 + 10x + 8
\]

This is the final simplified expression.