algebra tiles to find $$ \left(8 x^{2}-10 x+4\right)-\left(4 x^{2}+1\right) $$

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To subtract the polynomials $$ (8x^{2} - 10x + 4) - (4x^{2} + 1) $$ using algebra tiles, follow these steps:

### **1. Understanding Algebra Tiles:**
Algebra tiles are visual tools that represent different parts of a polynomial:
- **$$x^{2}$$ tiles:** Typically larger squares.
- **$$x$$ tiles:** Rectangles.
- **Constant tiles:** Small squares.

For subtraction, you'll remove the tiles representing the second polynomial from the first.

### **2. Represent Each Polynomial with Algebra Tiles:**

**First Polynomial: $$8x^{2} - 10x + 4$$**
- **$$8x^{2}$$ tiles:** 8 large square tiles.
- **$$-10x$$ tiles:** 10 negative rectangle tiles (often represented with a different color or marked with a negative sign).
- **$$+4$$ tiles:** 4 small square tiles.

**Second Polynomial: $$4x^{2} + 1$$**
- **$$4x^{2}$$ tiles:** 4 large square tiles.
- **$$+1$$ tile:** 1 small square tile.

### **3. Subtract the Second Polynomial:**
To subtract $$ (4x^{2} + 1) $$, remove the corresponding tiles from the first polynomial:
- **Remove $$4x^{2}$$ tiles:** Subtract 4 large square tiles from the 8.
- **Remove $$+1$$ tile:** Subtract 1 small square tile from the 4.

### **4. Calculate the Remaining Tiles:**
- **$$x^{2}$$ tiles:** $$8x^{2} - 4x^{2} = 4x^{2}$$
- **$$x$$ tiles:** No $$x$$ tiles to remove from the second polynomial, so it remains $$-10x$$.
- **Constant tiles:** $$4 - 1 = 3$$

### **5. Combine the Results:**
After subtraction, the resulting polynomial is:
$$
4x^{2} - 10x + 3
$$

### **Final Answer:**
$$
(8x^{2} - 10x + 4) - (4x^{2} + 1) = 4x^{2} - 10x + 3
$$
The result of the subtraction is $$4x^{2} - 10x + 3$$.

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