1. Draw an algebra tile model for the polynomial in simplified form:
8x^2 - 4x -3x^2 + 6 + 2x -7
8 big blue squares, 4 bars, 3 big red squares, 6 little yellow squares, 2 green bars, 7 little red bars;
(is this correct?)
2.Study the diagram of algebra tiles below.
3 big blue squares, 2 big red squares, 4 green bars, 2 little yellow squares.
+
3 big blue squares, 1 big red squares, 2 green bars, 3 red bars, 5 little red squares.
A. Write a polynomial that represents the model.
3x^2-2x^2+4x+2
+ 3x^21x^2+2x-3x-5
B. Simplify the expression above.
x^2+4x+2
+ 2x^2-x-5
( is this correct)
1. There seems to be an error in your expression for the algebra tile model. Let's break it down and create the correct model:
Start by grouping the like terms together: 8x^2 - 3x^2 - 4x + 2x - 7 + 6
Now, let's create the algebra tile model representation for each term:
- 8x^2 can be represented by 8 big blue squares.
- (-3x^2) can be represented by 3 big red squares.
- (-4x) can be represented by 4 bars.
- (2x) can be represented by 2 green bars.
- (-7) can be represented by 7 little red bars.
- (+6) can be represented by 6 little yellow squares.
Therefore, the correct algebra tile model for the polynomial is:
8 big blue squares - 4 bars - 3 big red squares + 6 little yellow squares + 2 green bars - 7 little red bars.
2. Let's go through the steps to correctly identify the polynomial that represents the given algebra tile model:
From the diagram, we can see that we have the following algebra tiles:
- 3 big blue squares
- 2 big red squares
- 4 green bars
- 2 little yellow squares
To write the polynomial, we need to identify the terms for each type of tile and combine like terms:
- The big blue squares represent x^2, so we have 3x^2.
- The big red squares also represent x^2, so we have 2x^2.
- The green bars represent x, so we have 4x.
- The little yellow squares represent 1, so we have 2.
Putting it all together, the polynomial that represents the model is:
3x^2 + 2x^2 + 4x + 2.
Now let's move on to simplifying the expression:
- Combine the like terms:
3x^2 + 2x^2 + 4x + 2 = 5x^2 + 4x + 2.
So the simplified expression is:
5x^2 + 4x + 2.
Therefore, the expressions you provided for both the polynomial representation and the simplified expression are incorrect. The correct answers are:
A. The polynomial model is 3x^2 + 2x^2 + 4x + 2.
B. The simplified expression is 5x^2 + 4x + 2.