SUP03-07

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\[\begin{aligned} A(x) &= \underline{(2x+1)}^2 - (3x+5)\underline{(2x + 1)}& \\ &=(2x+1)\big[(2x+1) - (3x+5)\big]& \\ &=(2x+1)(2x+1-3x-5)& \\ &=(2x+1)(-x-4)& \end{aligned}\] \[\begin{aligned} B(x) &= (3x-1)^2 - (2x+1)^2& \\ &=\big[(3x-1) - (2x+1)\big]\big[(3x-1)+(2x+1)\big]& \\ &=(3x-1 - 2x - 1)(3x + 1 + 2x + 1)& \\ &=(x - 2)(5x)& \\ &=5x(x-2).& \end{aligned}\] \[\begin{aligned} C(x) &= (x+4)^2 - (2x - 6)^2& \\ &= \big[(x+4)-(2x-6)\big]\big[(x+4) + (2x - 6)\big]& \\ &=(x+4-2x + 6)(x + 4 +2x -6)& \\ &=(-x+10)(3x - 2).& \end{aligned}\] \[\begin{aligned} D(x) &= (-2x+3)^2 - \frac 14x^2& \\ &= (-2x+3)^2 - \left(\frac 12x\right)^2& \\ &=\left[-(2x+3) - \frac 12x\right]\left[(-2x+3) + \frac 12x\right]& \\ &=\left(-2x + 3 - \frac 12x\right)\left(-2x + 3 + \frac 12x\right)& \\ &=\left(-\frac52x + 3\right)\left(-\frac 32x + 3\right).& \end{aligned}\] \[\begin{aligned} E(x) &= 4(x+2)^2 - 9(2x+1)^2& \\ &=\big[2(x+2)\big]^2 - \big[3(2x+1)\big]^2& \\ &=\big[2(x+2) - 3(2x+1)\big]\big[2(x+2) + 3(2x+1)\big]& \\ &=(2x + 4 - 6x - 3)(2x + 4 + 6x + 3)& \\ &=(-4x + 1)(8x + 7).& \end{aligned}\] \[\begin{aligned} F(x) &= \underline{(x-2)}(2x+5) + 4\underline{(x-2)}(x-1)& \\ &=(x-2)\big[(2x+5) + 4(x-1)\big]& \\ &=(x-2)(2x + 5 + 4x - 4)& \\ &=(x-2)(6x + 1).& \end{aligned}\]

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code : 184