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\(x^{m+1}-x^m=x^m.x-x^m=x^m.\left(x-1\right)\)
\(x^{m+2}-x^m=x^m.x^2-x^m=x^m.\left(x^2-1\right)\)
\(x^{m+2}-x^2=x^m.x^2-x^2=x^2.\left(x^m-1\right)\)
Bài làm :
\(x^{m+1}-x^m=x^m.x-x^m=x^m.\left(x-1\right)\)
\(x^{m+2}-x^m=x^m.x^2-x^m=x^m.\left(x^2-1\right)\)
\(x^{m+2}-x^2=x^m.x^2-x^2=x^2.\left(x^m-1\right)\)
\(2x^2-x^2-3x-1\)
\(=x^2-3x-1\)
\(=\frac{1}{4}\left(4x^2-12x-4\right)\)
\(=\frac{-1}{4}\left[13-\left(4x-12x+9\right)\right]\)
\(=-\frac{1}{4}\left[13-\left(2x-3\right)^2\right]\)
\(=-\frac{1}{4}\left(\sqrt{13}-2x+3\right)\left(\sqrt{13}+2x-3\right)\)
\(x^2+7x+6\)
\(=x^2+x+6x+6\)
\(=x\left(x+1\right)+6\left(x+1\right)\)
\(=\left(x+1\right).\left(x+6\right)\)
\(\left(3x-2\right)\left(4x-3\right)-\left(2-3x\right)\left(x-1\right)-2\left(3x-2\right)\left(x+1\right)\)
\(=\)\(\left(3x-2\right)\left(4x-3\right)+\left(3x-2\right)\left(x-1\right)-\left(3x-2\right)\left(2x+2\right)\)
\(=\)\(\left(3x-2\right)\left(4x-3+x-1-2x-2\right)\)
\(=\)\(\left(3x-2\right)\left(3x-6\right)\)
\(=\)\(3\left(x-2\right)\left(3x-2\right)\)
Chúc bạn học tốt ~
\(\left(x+1\right)^2-\left(x-1\right)^2\)
\(\Leftrightarrow\left(x+1-x+1\right)\left(x+1+x-1\right)\)
\(\Leftrightarrow2.2x=4x\)
p/s tham khảo nha
\(a^2-b^2-a+b\)
\(\Leftrightarrow\left(a-b\right)\left(a+b\right)-\left(a-b\right)\)
\(\Leftrightarrow\left(a-b\right)\left(a+b-1\right)\)
p/s tham khảo
Ta có : x2 + x - 6
= x2 + 3x - 2x - 6
= (x2 + 3x) - (2x + 6)
= x(x + 3) - 2(x + 3)
= (x - 2)(x + 3)
x^2 + x - 4 -2 = ( x^2 - 4 ) + ( x - 2 )
= ( x - 2 ).( x + 2 ) + ( x - 2 )
= ( x - 2 ).( x + 2 + 1 )
= ( x - 2 ).( x + 3 )