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=(a - b) (a2 - b2)
= (a - b) (a - b) (a + b)
= (a - b)2(a + b)
\(\left(a+b+c\right)\left(ab+bc+ca\right)-abc\)
\(=\left(a+b+c\right)\left(ab+bc\right)+\left(a+b+c\right)ac-abc\)
\(=\left(ab+b^2+bc\right)\left(a+c\right)+\left(a+c\right)ac+abc-abc\)
\(=\left(a+c\right)\left(ab+b^2+bc+ac\right)\)
\(=\left(a+b\right)\left(b+c\right)\left(c+a\right)\)
2.Tim x
a,(2x+1)2-4(x+2)2=9
<=> (4x2+4x+1)-4(x2+4x+4)=9
<=> -12x-15=9
<=> -12x=24
<=> x=-2
\(1a,\)\(\left(x^2-0,1\right)=\left(x-\sqrt{0,1}\right)\left(x+\sqrt{0,1}\right)\)
\(1b,\)\(\left(2a^2+b^2\right)^2=\left(2a^2\right)^2+2.2a^2.b^2+\left(b^2\right)^2=4a^4+4a^2b^2+b^4\)
\(1c,\)\(\left(a^2+5\right)\left(5-a^2\right)=\left(5+a^2\right)\left(5-a^2\right)=25-x^4\)
c) \(VT=\left(a+b+c\right)^3-a^3-b^3-c^3\)
\(=\left(a+b\right)^3+3c\left(a+b\right)\left(a+b+c\right)+c^3-a^3-b^3-c^3\)
\(=a^3+b^3+c^3+3ab\left(a+b\right)+3c\left(a+b\right)\left(a+b+c\right)-a^3-b^3-c^3\)
\(=3\left(a+b\right)\left[ab+c\left(a+b+c\right)\right]\)
\(=3\left(a+b\right)\left(ab+ac+bc+c^2\right)\)
\(=3\left(a+b\right)\left(b+c\right)\left(c+a\right)=VP\)
d) \(VT=a^3+b^3+c^3-3abc\)
\(=\left(a+b\right)^3-3ab\left(a+b\right)+c^3-3abc\)
\(=\left(a+b+c\right)\left[\left(a+b\right)^2-\left(a+b\right)c+c^2\right]-3ab\left(a+b+c\right)\)
\(=\left(a+b+c\right)\left(a^2+b^2+c^2-ab-bc-ca\right)=VP\)
I don't now
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1. (a+b).(a+b)=\(\left(a+b\right)^2\)
2. (a-b).(a-b)=\(\left(a-b\right)^2\)
3. (a+b).(a-b)=\(a^2-b^2\)
4. (a+b).(a2- ab +b2)=\(a^3+b^3\)
5. (a-b).(a2 + ab + b2)=\(a^3-b^3\)
6. (a+b).(a2+ 2ab + b2)=\(\left(a+b\right).\left(a+b\right)^2=\left(a+b\right)^3\)
7. (a-b).(a2- 2ab + b2)=\(\left(a-b\right).\left(a-b\right)^2=\left(a-b\right)^3\)