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\(1.z^2-6z+5-t^2-4t\)
\(=\left(z^2-6z+9\right)-\left(t^2+4t+4\right)\)
\(=\left(z-3\right)^2-\left(t+2\right)^2\)
\(3,x^2-2xy+2y^2+2y+1\)
\(=\left(x^2-2xy+y^2\right)+\left(y^2+2y+1\right)\)
\(=\left(x-y\right)^2+\left(y+1\right)^2\)
\(1,\)\(4x^2-4x+y^2+2y+2\)
\(=4x^2+4x+1+y^2+2y+1\)
\(=\left[\left(2x\right)^2-2.2x+1\right]+\left(y^2+2.y.1+1^2\right)\)
\(=\left(2x-1\right)^2+\left(y+1\right)^2\)
\(2,\)\(a^2-4ab+5b^2-4bc+4c^2\)
\(=a^2-4ab+4b^2+b^2-4bc+4c^2\)
\(=\left[a^2-2.a.2b+\left(2b\right)^2\right]+\left[b^2-2.b.2c+\left(2c\right)^2\right]\)
\(=\left(a-2b\right)^2+\left(b-2c\right)^2\)
\(3,\)\(16x^2+5+8x-4y+y^2\)
\(=16x^2+8x+1+y^2-4y+4\)
\(=\left[\left(4x\right)^2+2.4x.1+1^2\right]+\left[y^2-2.y.2+2^2\right]\)
\(=\left(4x+1\right)^2+\left(y-2\right)^2\)
Bài 3a)
\(a+b+c=0\Leftrightarrow a+b=-c\Leftrightarrow a^3+b^3+3ab\left(a+b\right)=-c^3\)
\(\Leftrightarrow a^3+b^3+c^3=-3ab\left(a+b\right)\)
mà \(a+b=-c\Rightarrow a^3+b^3+c^3=3abc\)
\(45^2+40^2-10^2+80.45\)
\(=\left(45+40\right)^2-10^2\)
\(=\left(45+40-10\right)\left(45+40+10\right)\)
\(=75.95=7125\)
\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(=\left(2^{32}-1\right)\)
1.
(a+1)2=a2+2a+1
2.
x2+4x+4=x2+2.x.2+22=(x+2)2
3.
512=(50+1)2=502+2.50+1=2500+100+1=2601
3012=(300+1)2=3002+2.300+1=90000+600+1=90601
1:a=-1
2:(x+2)2
3:2601;90601