Use algebra tiles to find \( \left(-10 x^{2}+4 x+7\right)-\left(2 x^{2}+3 x\right) \)

To solve the expression \( \left(-10x^{2}+4x+7\right) - \left(2x^{2}+3x\right) \) using algebra tiles, you would start by representing the first polynomial using the tiles: 1. For \( -10x^2 \), you would use 10 tiles that represent \( x^2 \) with a negative sign. 2. For \( +4x \), you would use 4 positive \( x \) tiles. 3. For \( +7 \), you would use 7 positive unit tiles. Now, for the second polynomial \( 2x^{2} + 3x \): 1. Use 2 tiles representing \( x^2 \) but place them as positive. 2. Use 3 positive \( x \) tiles. Next, to carry out the subtraction, you remove the tiles corresponding to the second polynomial from those of the first. When you subtract \( 2x^2 \) and \( 3x \): - From the \( -10x^2 \) tiles, when you remove 2 positive \( x^2 \) tiles, you are left with \( -12x^2 \) (10 remove 2 = 12 negative). - From the \( +4x \) tiles, when removing 3 positive \( x \) tiles, you are left with \( +1x \) (4 remove 3 = 1 positive). - The \( +7 \) unit tiles remain unchanged as you are not subtracting any unit tiles. Putting it all together, the result is: \[ -12x^{2} + 1x + 7 \] Thus, the simplified answer is \( -12x^2 + x + 7 \).