[tex]a)\, (-72x^2+48x^4-36x^3):(-4x^2)=[/tex]
[tex]\frac{-72x^2+48x^4-36x^3}{-4x^2} =\frac{4x^2\cdot(-18+12x^2-9x)}{-4x^2}^{(-4}[/tex]
[tex]= \frac{-x^2\cdot (-18+12x^2-9x)}{x^2} ^{x^2)}=-(-18+12x^2-9x)[/tex]
[tex]\implies 18-12x^2+9x=-12x^2+9x+18[/tex]
[tex]b)\, \sqrt{3} \,(2\sqrt{3} -x)+\sqrt{6} \,(3\sqrt{2}\, x+\sqrt{3} )=[/tex]
[tex]6-\sqrt{3} \,x+\sqrt{6} \,(3\sqrt{2} \,x+\sqrt{3} )=[/tex]
[tex]6-\sqrt{3} \,x+3\sqrt{12} \,x+\sqrt{18} =[/tex]
[tex]6-\sqrt{3} \,x + 3\cdot2\sqrt{3} \,x+3\sqrt{2} =[/tex]
[tex]6-\sqrt{3} \,x+6\sqrt{3} \,x+3\sqrt{2} =6+5\sqrt{3} x+3\sqrt{2}[/tex]
[tex]c)\,(21x^3-14x^2):(-7x^2)+(x-1)(x+2)=[/tex]
[tex]\frac{21x^3-14x^2}{-7x^2} +x^2+2x-x-2=[/tex]
[tex]\frac{7x^2(3x-2)}{-7x^2}^{(-7x^2} +x^2+2x-x-2=[/tex]
[tex]-(3x-2)+x^2+2x-x-2=[/tex]
[tex]-3x+2+x^2+x-2=-3x+x^2+x=-2x+x^2[/tex]
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[tex]x^{m+1}+x^m+x^{m-1}=[/tex]
[tex]x^{m-1}(x^{m+1-(m-1)}+x^{m-(m-1)}+x^{x-1-(m-1)})=[/tex]
[tex]x^{m-1}(m^{m+1-m+1}+x^{m-m+1}+x^{m-1-m+1})=[/tex]
[tex]x^{m-1}(x^{1+1}+x^1+x^0)\implies = x^{m-1}(x^2+x+1)[/tex]
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[tex]x^{2014}-x^{2013}-x^{2012}=[/tex]
[tex]x^{2012}\cdot x^2 -x^{2012}\cdot x^1 - x^{2012}\cdot x^0=[/tex]
[tex]x^{2012}(x^2-x^1-x^0) \implies x^{2012}(x^2-x-1)[/tex]
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[tex](2x+3)^2+(2x-3)^2\implies folosind\:formula\: (a+b)^2=a^2+2ab+b^2[/tex]
[tex]\implies (2x+3)^2=(2x)^2+2\cdot2x\cdot3+3^2=4x^2+12x+9[/tex]
[tex]\implies (2x-3)^2=(2x)^2-2\cdot2x\cdot3+3^2=4x^2-12x+9[/tex]
[tex](2x+3)^2+(2x-3)^2=4x^2+12x+9+4x^2-12x+9[/tex]
[tex]\implies 4x^2+9+4x^2+9=8x^2+18[/tex]
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[tex]11^2+121b^2+22c^2= 11^2+11^2b^2+2 \cdot 11c^2[/tex]
[tex]\implies = 11(11+11b^2+2c^2)[/tex]
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[tex]ab^2+a^2b+ab=ab\,(b+a+1)[/tex]
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[tex]x^{2015}+x^{2014}+x^{2013}=x^{2013}\cdot x^2+2^{2013}\cdot x^1 + x^{2013}\cdot x^0[/tex]
[tex]\implies = x^{2013}(x^2+x+1)[/tex]
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[tex]2015\,x^{2017}+2015\,x^{2016}=2015\,x^{2016}(x-1)[/tex]
