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1.\(x^3+6x^2+12xy+8=x^3+3.2x^2+3.2^2x+2^3=\left(x+2\right)^3\)
3.\(x^4+2x^3+x^2-y^2=\left(x^2\right)^2+2x^2.x+x^2-y^2\)\(=\left(x^2+x\right)^2-y^2=\left(x^2+x-y\right)\left(x^2+x+y\right)\)
k mình nha bn !!!!!!! cái 2 bn xem lại đề đi, rồi mình giải cho
x10+x5+1
= x10+x9+x8-x9-x8-x7+x7+x6+x5-x6-x5-x4+x5+x4+x3-x3-x2-x+x2+x+1
= x8(x2+x+1)-x7(x2+x+1)+x5(x2+x+1)-x4(x2+x+1)+x3(x2+x+1)-x(x2+x+1)+(x2+x+1)
= (x2+x+1)(x8-x7+x5-x4+x3-x+1)
2: \(=a^2\left(a+3\right)+4\left(a+3\right)=\left(a+3\right)\left(a^2+4\right)\)
3: \(=\left(2a-1\right)^2-4b^2\)
\(=\left(2a-1-2b\right)\left(2a-1+2b\right)\)
4: \(=-\left(x^2+x-2\right)=-\left(x+2\right)\left(x-1\right)\)
5: \(=7\left(x^2-2xy^2+y^4\right)=7\left(x-y^2\right)^2\)
6: \(=\left(x+2\right)^2-y^2=\left(x+2+y\right)\left(x+2-y\right)\)
xm+2+xm = xm(x^2 + 1)
xx+1-xx-1 = x^x . x - x^x - \(\frac{x^x}{x^x}\)=x^x ( x - 1 - 1/x^x) ( cái này mik ko bik đúng hay sai)
a^3 - 1 = a^3 - 1^3 = ( a-1)(a^2 + a + 1)
a^5 - b^5 = \(\left(\sqrt{a^5}\right)^2-\left(\sqrt{b^5}\right)^2=\left(\sqrt{a^5}+\sqrt{b^5}\right)\left(\sqrt{a^5}-\sqrt{b^5}\right)\)
\(x^7+x^5+x^4+x^3+x^2+1\)
\(=x^7+x^6-x^6-x^5+2x^5+2x^4-x^4-x^3+2x^3+2x^2-x^2-x+x+1\)
\(=\left(x^7+x^6\right)-\left(x^6+x^5\right)+\left(2x^5+2x^4\right)-\left(x^4+x^3\right)+\left(2x^3+2x^2\right)-\left(x^2+x\right)+\left(x+1\right)\)
\(=x^6.\left(x+1\right)-x^5.\left(x+1\right)+2x^4\left(x+1\right)-x^3\left(x+1\right)+2x^2\left(x+1\right)-x\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^6-x^5+2x^4-x^3+2x^2-x+1\right)\)
\(x5+x-1 = x5-x4+x3+x4-x3+x2-x2+x-1 = x3(x2-x+1)+x2(x2-x+1)-(x2-x+1) = (x2-x+1)(x3+x2-1) \)
hc tốt nha !!!!!!!!!
x8 + x7 +1=x8+x7+x6+x5+x4+x3+x2+x+1-x6-x5-x4-x3-x2-x
=x6(x2+x+1)+x3(x2+x+1)+(x2+x+1)-x4(x2+x+1)-x(x2+x+1)
=(x2+x+1)(x6+x3-x4-x)
=(x2+x+1)[x3(x3+1)-x(x3+1)]
=(x2+x+1)(x3+1)(x3-x)
=x(x2+x+1)(x+1)(x2-x+1)(x2-1)
=x(x2+x+1)(x+1)(x2-x+1)(x+1)(x-1)
=x(x2+x+1)(x+1)2(x2-x+1)(x-1)
x5 + x +1
= x5 + x + x2 + 1 - x2
= (x5 - x2 ) + (x2 + x+1 )
=x2(x3 -1) +(x2 + x+1 )
=x2(x-1)(x2 + x+1) + (x2 + x+1 )
=[x2(x-1)+1](x2 + x+1 )
=(x3 - x2 +1)(x2 + x+1 )