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

Let's expand each of the given expressions step by step.<br /><br />1. \((x-8)(x+1)\)<br /><br />Using the distributive property (also known as the FOIL method for binomials):<br />\[<br />(x-8)(x+1) = x(x+1) - 8(x+1)<br />\]<br />\[<br />= x^2 + x - 8x - 8<br />\]<br />\[<br />= x^2 - 7x - 8<br />\]<br /><br />2. \((x-3)(x-6)\)<br /><br />Again, using the distributive property:<br />\[<br />(x-3)(x-6) = x(x-6) - 3(x-6)<br />\]<br />\[<br />= x^2 - 6x - 3x + 18<br />\]<br />\[<br />= x^2 - 9x + 18<br />\]<br /><br />3. \((2x+9)(x-2)\)<br /><br />Using the distributive property:<br />\[<br />(2x+9)(x-2) = 2x(x-2) + 9(x-2)<br />\]<br />\[<br />= 2x^2 - 4x + 9x - 18<br />\]<br />\[<br />= 2x^2 + 5x - 18<br />\]<br /><br />4. \((3x+1)(2x+4)\)<br /><br />Using the distributive property:<br />\[<br />(3x+1)(2x+4) = 3x(2x+4) + 1(2x+4)<br />\]<br />\[<br />= 6x^2 + 12x + 2x + 4<br />\]<br />\[<br />= 6x^2 + 14x + 4<br />\]<br /><br />So, the expanded forms of the given expressions are:<br />1. \(x^2 - 7x - 8\)<br />2. \(x^2 - 9x + 18\)<br />3. \(2x^2 + 5x - 18\)<br />4. \(6x^2 + 14x + 4\)