Question
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Answer
Solution
To solve the expression
using algebra tiles, let’s break it down step by step.
Step 1: Understand the Components
-
First Polynomial:
-
: Represents seven tiles. -
: Represents five tiles. -
: Represents six negative unit tiles.
-
-
Second Polynomial (to be subtracted):
-
: Represents ten negative tiles. -
: Represents three negative unit tiles.
-
Step 2: Subtract the Second Polynomial
Subtracting
is equivalent to adding its opposite:
Step 3: Combine Like Terms Using Algebra Tiles
-
Combine
Terms: -
remains as there are no other terms to combine.
-
-
Combine
Terms: -
-
Combine Constant Terms:
-
Step 4: Write the Final Expression
Combine all the simplified terms:
Visual Representation with Algebra Tiles
While I can’t provide a visual diagram here, here’s how you can imagine the tiles:
-
Positive Tiles:
- 7
tiles - 15
tiles
- 7
-
Negative Tiles:
- 3 negative unit tiles
Arrange the tiles accordingly to represent the final simplified expression.
Final Answer
Answered by UpStudy AI and reviewed by a Professional Tutor
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The Deep Dive
First, let’s combine the expressions using algebra tiles. You can visualize
as 7 large tiles (representing
), 5 medium tiles (representing
), and 6 small red tiles (representing -6). Then, adding
means you’ll have 10 more medium tiles and 3 additional small tiles, but they’ll be green (representing +3).
Now combine them: You have 7 large tiles, (still 7), 5 medium tiles plus 10 more giving you 15 medium tiles, and -6 plus 3 gives you -3. Thus, the simplified expression is:
Now, if you wanted to express this in algebraic form, it would look great as
! Algebra tiles make combining like terms a visual breeze!