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a) \(x^2+10x+26+y^2+2y\)
\(=\left(x^2+10x+25\right)+\left(y^2+2y+1\right)\)
\(\left(x+5\right)^2+\left(y+1\right)^2\)
b) \(x^2-2xy+2y^2+2y+1\)
\(=\left(x^2-2xy+y^2\right)+\left(y^2+2y+1\right)\)
\(=\left(x-y\right)^2+\left(y+1\right)^2\)
c) \(z^2-6z+13+t^2+4t\)
\(=\left(z^2-6x+9\right)+\left(t^2+4t+4\right)\)
\(=\left(z-3\right)^2+\left(t+2\right)^2\)
d) \(4x^2-2z^2-2xz-2z+1\)
\(=\left(4x^2-4xz+z^2\right)+\left(z^2-2z+1\right)\)
\(=\left(2x-z\right)^2+\left(z-1\right)^2\)
\(\dfrac{z^8+11z^4+30}{18z^2+12z+2}\cdot\dfrac{24z^2+8z}{z^2+6z}\)
\(=\dfrac{\left(z^4+6\right)\left(z^4+5\right)}{2\left(9z^2+6z+1\right)}\cdot\dfrac{8z\left(3z+1\right)}{z\left(z+6\right)}\)
\(=\dfrac{\left(z^4+6\right)\left(z^4+5\right)}{\left(3z+1\right)^2}\cdot\dfrac{4\left(3z+1\right)}{z+6}\)
\(=\dfrac{\left(z^4+6\right)\left(z^4+5\right)\cdot4}{\left(3z+1\right)\left(z+6\right)}\)
z2-6z+5-t2-4t=z2-6z+9-t2-4t-4
=(z-3)2-(t2+4t+4)
=(z-3)2-(t+2)2
=[(z-3)+(t+2)][(z-3)-(t+2)]
=(z-3+t+2)(z-3-t-2)
=(z+t-1)(z-t-5)
\(\left(1+\frac{1}{3}\right)\left(1+\frac{1}{8}\right)...\left(1+\frac{1}{n^2+2n}\right)\)
\(=\frac{2^2}{2}.\frac{3^2}{8}.....\frac{\left(n+1\right)^2}{n\left(n+2\right)}\)
\(=\frac{2.2.3.3.....\left(n+1\right)\left(n+1\right)}{1.3.2.4.....n\left(n+1\right)}\)
\(=\frac{2.3....\left(n+1\right)}{1.2.3....n}.\frac{2.3...\left(n+1\right)}{3.4.5....\left(n+2\right)}\)
\(=\left(n+1\right)\frac{2}{n+2}\)
\(=\frac{2n+2}{n+2}\)
mình mới học lớp 7 thui à
Nếu lớp 8 thì sẽ giúp bạn liền