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=\(x^2-2xy+y^2-\left(z^2-2zt+t^2\right)\))
=\(\left(x-y\right)^2\)- \(\left(z-t\right)^2\)
a) \(x^2-x-y^2+y\)
\(=x\left(x-1\right)-y\left(y-1\right)\)
\(=\left(x-1\right)\left(x-y\right)\)
b) \(x^2-2xy-z^2+y^2\)
\(=\left(x^2-2xy+y^2\right)-z^2\)
\(=\left(x-y\right)^2-z^2\)
\(=\left(x-y-z\right)\left(x-y+z\right)\)
c) \(5x-5y+ax-ay\)
\(=5\left(x-y\right)+a\left(x-y\right)\)
\(=\left(x-y\right)\left(5+a\right)\)
x2-2xy+y2-z2+2zt-t2
=(x2-2xy+y2)-(z2-2zt+t2)
=(x-y)2-(z-t)2
=(x-y+z-t)(x-y-z+t)
x2 – 2xy + y2 – z2 + 2zt – t2 = (x2 – 2xy + y2) – (z2 – 2zt + t2)
= (x – y)2 – (z – t)2
= [(x – y) – (z – t)] . [(x – y) + (z – t)]
= (x – y – z + t)(x – y + z – t)
1)\(x^4+2x^3+x^2\)
=\(\left(x^4+x^3\right)+\left(x^3+x^2\right)\)đật nhân tử chung ra
=\(x^2\left(x+1\right)^2\)
2) pt => \(\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
=\(\left(x+y\right)^3-\left(x+y\right)\)
=\(\left(x+y\right)\left(\left(x+y\right)^2+1\right)\)
3)chia tất cả cho 5 pt => \(x^2-2xy+y^2-4x^2\)
=\(\left(x+y\right)^2-4z^2\)
=\(\left(x+y+2z\right)\left(x+y-2z\right)\)
4)pt => \(2\left(x-y\right)-\left(x^2-2xy+y^2\right)\)
=\(2\left(x-y\right)-\left(x-y\right)^2\)
=\(\left(x-y\right)\left(2-x+y\right)\)
k chi nha
1/ \(3x^2+6x+3-3y^2=3x^2+3x+3x+3-3y^2\)
\(=3\left(x^2+2x+1-y^2\right)\)
\(=3\left[\left(x^2+2x+1\right)-y^2\right]\)
\(=3\left[\left(x+1\right)^2-y^2\right]\)
\(=3\left(x+1-y\right)\left(x+1+y\right)\)
2/ \(25-x^2-y^2+2xy=5^2-\left(x^2+y^2-2xy\right)\)
\(=5^2-\left(x-y\right)^2\)
\(=\left[5-\left(x-y\right)\right]\left(5+x+y\right)\)
\(=\left(5-x+y\right)\left(5+x+y\right)\)
3/ \(3x-3y-x^2+2xy-y^2=3\left(x-y\right)-\left(x^2-2xy+y^2\right)\)
\(=3\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(x-y\right)\left[3-\left(x-y\right)\right]\)
\(=\left(x-y\right)\left(3-x+y\right)\)
= (3x + 1 - x - 1)(3x + 1 + x + 1)
= 2x(4x + 2)
Em áp dụng hđt số 3 trong sgk nhé.
Đề sai nhé .Sửu lại
\(x^2-4x^2y^2+4+4x\)
\(=\left(x^2+4x+4\right)-4x^2y^2\)
\(=\left(x+2\right)^2-\left(2xy\right)^2\)
\(=\left(x+2+2xy\right)\left(x+2-2xy\right)\)
1) \(x^2-2x-4y^2-4y\)
\(=\left[x^2-\left(2y\right)^2\right]-\left(2x+4y\right)\)
\(=\left(x+2y\right)\left(x-2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
2) \(x^4+2x^3-4x-4\)
\(=\left(x^4-4\right)+\left(2x^3-4x\right)\)
\(=\left(x^2+2\right)\left(x^2-2\right)+2x\left(x^2-2\right)\)
\(=\left(x^2-2\right)\left(x^2+2+2x\right)\)
3) \(x^2\left(1-x^2\right)-4x+4x^2\)
\(=x^2\left(1+x\right)\left(1-x\right)+4x\left(x-1\right)\)
\(=x^2\left(1+x\right)\left(1-x\right)-4x\left(1-x\right)\)
\(=\left(1-x\right)\left[x^2\left(1+x\right)-4x\right]\)
1) \(25-x^2-y^2+2xy=5^2-\left(x^2-2xy+y^2\right)=5^2-\left(x-y\right)^2\)\(=\left(5-x+y\right)\left(5+x-y\right)\)
2) \(3x-3y-x^2+2xy-y^2\)\(=3\left(x-y\right)-\left(x^2-2xy+y^2\right)\)\(=3\left(x-y\right)-\left(x-y\right)^2\)\(=\left(x-y\right)\left(3-x+y\right)\)
1) \(25-x^2-y^2+2xy\)
\(=5^2-\left(x^2+y^2-2xy\right)\)
\(=5^2-\left(x-y\right)^2\)
\(=\left(x-y-5\right)\left(x-y+5\right)\)
2) \(3x-3y-x^2+2xy-y^2\)
\(=3\left(x-y\right)-\left(x^2-2xy+y^2\right)\)
\(=3\left(x-y\right)-\left(x-y\right)\left(x-y\right)\)
\(=\left(3-x+y\right)\left(x-y\right)\)
x2 - 2xy + y2 - z2 + 2zt - t2
= (x2 - 2xy + y2) - (z2 - 2zt + t2)
= (x-y)^2 - (z - t)^2
= (x-y+z-t)(x-y-z-t)