AUT01-15

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a. Factorisons : \[\begin{aligned} &(4x+5)\underline{(x+3)} - 3\underline{(x+3)}(x-2)& \\ =&(x+3)\big[(4x+5) - 3(x-2)\big]& \\ =&(x+3)(4x+5 -3x + 6)& \\ =&(x+3)(2x+11).& \end{aligned}\]

b. Factorisons : \[\begin{aligned} &(x+3)\underline{(2x+3)} - \underline{(2x+3)}& \\ =&(2x+3)\big[(x+3) - 1\big]& \\ =&(2x+3)(x+3-1)& \\ =&(2x+3)(x+2).& \end{aligned}\]

c. Factorisons : \[\begin{aligned} &\underline{(3y-5)^2} + 2\underline{(3y-5)}& \\ =&(3y-5)\big[(3y-5) + 2\big]& \\ =&(3y-5)(3y-5+2)& \\ =&(3y-5)(\underline{3}y-\underline{3})& \\ =&(3y - 5)3(y - 1)& \\ =&3(3y-5)(y-1).& \end{aligned}\]

d. Factorisons : \[\begin{aligned} &8x^4 - 6x^3 + 4x^2& \\ =&\underline{2x^2} \cdot 4x^2 - \underline{2x^2}\cdot 3x + \underline{2x^2} \cdot 2& \\ =&2x^2(4x^2 - 3x + 2).& \end{aligned}\]

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code : 169