Question

expand 1) (x+6)(x-4)(x-2) 2) (x-8)(x+10) 3) (x - 1/X + 5)^2 please answer fast , and answer only relevant to the question chapter : expansions grade 9

Answer 1

1) $(x+6)(x-4)(x-2)$ => $(x^2 - 4x + 6x - 24)(x-2)$

=> $(x^2+ 2x - 24)(x-2)$ => $x^3- 2x^2 + 2x^2 -4x -24x +48$

=> $x^3 -28x +48$

2) $(x-8)(x+10)$ => $x^2 + 10x - 8x -80$ => $x^2 + 2x -80$

3) $(x - \frac{1}{x} + 5)^2$ => $(\frac{x^2 - 1 + 5x}{x} )^2$ =>$(\frac{x^4 + 1 + 25x^2 -2x^4 -10x + 10x^3 }{x^2} )$

----> ${(a+b+c)^2 = a^2 b^2 + c^2 + 2ab + 2bc + 2ca }$ <----

=>$(\frac{-x^4 + 1 + 25x^2 -10x + 10x^3 }{x^2} )$ => $(\frac{-x^4 + 10x^3 + 25x^2-10x + 1 }{x^2} )$

=>$(\frac{x^4 - 10x^3 - 25x^2+10x - 1 }{x^2} )$ => $x^2 -10x -25 + \frac{10}{x} - \frac{1}{x^2}$

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