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a ) \(x^3z+x^2yz-x^2z^2-xyz^2=\left(x^3z-x^2z^2\right)+\left(x^2yz-xyz^2\right)\)
\(=\left(x-z\right)\left(x^2z+xyz\right)\)
\(=xz\left(x-z\right)\left(x+y\right)\)
b ) \(p^{m+2}.q-p^{m+1}q^3-p^2q^{n+1}+pq^{n+3}\)
\(=p^{m+1}q\left(p-q^2\right)-pq^{n+1}\left(p-q^2\right)\)
\(=\left(p-q^2\right)\left(p^{m+1}q-pq^{n+1}\right)\)
\(=pq\left(p-q^2\right)\left(p^m-q^n\right)\)
25n(n-1)-50(n-1) luôn chia hết cho 150 với mọi n là số nguyên
giúp mình chứng minh nha . Cám ơn mấy bạn
\(x^4+x^2+1\)
\(=\left[\left(x^2\right)^2+2x^2.1+1^2\right]-x^2\)
\(=\left(x^2+1\right)^2-x^2\)
\(=\left(x^2+x+1\right)\left(x^2-x+1\right)\)
\(\left(x^2-8\right)^2+36\)
\(=x^4-16x^2+64+36\)
\(=\left[\left(x^2\right)^2-2.10x^2+10^2\right]-\left(2x\right)^2\)
\(=\left(x^2-10\right)^2-\left(2x\right)^2\)
\(=\left(x^2-10-2x\right)\left(x^2-10+2x\right)\)
\(4x^4+81\)
\(=\left[\left(2x^2\right)^2+2.2x^2.9+9^2\right]-\left(6x\right)^2\)
\(=\left(2x^2+9\right)-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right).\left(2x^2+9+6x\right)\)
Tham khảo nhé~
a) \(x^{m+2}-2x^m=x^m\left(x^2-2\right)\)
b) \(x^{k+1}-x^{k+2}=x^{k+1}\left(1-x\right)\)
a) xm+2 - 2xm = xm.x2 + 2.xm = xm( x2 - 2 ) = xm( x - √2 )( x + √2 )
b) xk+1 - xk+2 = xk+1 - xk+1.x = xk+1( 1 - x )
\(\left(x+1\right)^2-\left(x-1\right)^2\)
\(\Leftrightarrow\left(x+1-x+1\right)\left(x+1+x-1\right)\)
\(\Leftrightarrow2.2x=4x\)
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
1/ 2a + 2b = 2( a + b )
2/ 3a - 6b - 9c = 3( a - 2b - 3c )
3/ 5ax - 15ay + 20a = 5a( x - 3y + 4 )
4/ 3a2x - 6a2y + 12a = 3a( ax - 2ay + 4 )
5/ 4a( x - 5 ) - 2( 5 - x ) = 4a( x - 5 ) + 2( x - 5 ) = ( x - 5 )( 4a + 2 ) = ( x - 5 )2( 2a + 1 )
6. -3a( x - 3 ) + ( 3 - x ) = 3a( 3 - x ) + 1( 3 - x ) = ( 3a + 1 )( 3 - x )
7/ xm+1 - xm = xm( x + 1 )
8/ xm+2 - x2 = x2( xm - 1 )
\(x^{m+1}-x^m=x^m.x-x^m=x^m.\left(x-1\right)\)
\(x^{m+2}-x^m=x^m.x^2-x^m=x^m.\left(x^2-1\right)\)
\(x^{m+2}-x^2=x^m.x^2-x^2=x^2.\left(x^m-1\right)\)
Bài làm :
\(x^{m+1}-x^m=x^m.x-x^m=x^m.\left(x-1\right)\)
\(x^{m+2}-x^m=x^m.x^2-x^m=x^m.\left(x^2-1\right)\)
\(x^{m+2}-x^2=x^m.x^2-x^2=x^2.\left(x^m-1\right)\)