(x+3)(x+5)x^2 (x+2)(x+9)x^2 ) (x-8)(x+1) x ) - (x-3)(x-6) (2x+9)(x-2) (3x+1)(2x+4)

Let's expand each expression step by step:<br /><br />1. \((x+3)(x+5)x^2\)<br /> \[<br /> (x+3)(x+5) = x^2 + 8x + 15<br /> \]<br /> Then multiply by \(x^2\):<br /> \[<br /> (x^2 + 8x + 15)x^2 = x^4 + 8x^3 + 15x^2<br /> \]<br /><br />2. \((x+2)(x+9)x^2\)<br /> \[<br /> (x+2)(x+9) = x^2 + 11x + 18<br /> \]<br /> Then multiply by \(x^2\):<br /> \[<br /> (x^2 + 11x + 18)x^2 = x^4 + 11x^3 + 18x^2<br /> \]<br /><br />3. \((x-8)(x+1)x\)<br /> \[<br /> (x-8)(x+1) = x^2 - 7x - 8<br /> \]<br /> Then multiply by \(x\):<br /> \[<br /> (x^2 - 7x - 8)x = x^3 - 7x^2 - 8x<br /> \]<br /><br />4. \(-(x-3)(x-6)\)<br /> \[<br /> (x-3)(x-6) = x^2 - 9x + 18<br /> \]<br /> Then multiply by \(-1\):<br /> \[<br /> -(x^2 - 9x + 18) = -x^2 + 9x - 18<br /> \]<br /><br />5. \((2x+9)(x-2)\)<br /> \[<br /> (2x+9)(x-2) = 2x^2 - 4x + 9x - 18 = 2x^2 + 5x - 18<br /> \]<br /><br />6. \((3x+1)(2x+4)\)<br /> \[<br /> (3x+1)(2x+4) = 6x^2 + 12x + 2x + 4 = 6x^2 + 14x + 4<br /> \]<br /><br />So, the expanded forms are:<br /><br />1. \(x^4 + 8x^3 + 15x^2\)<br />2. \(x^4 + 11x^3 + 18x^2\)<br />3. \(x^3 - 7x^2 - 8x\)<br />4. \(-x^2 + 9x - 18\)<br />5. \(2x^2 + 5x - 18\)<br />6. \(6x^2 + 14x + 4\)